Elastic Behavior of Cross-Linked and Bundled Actin Networks

Abstract

Networks of cross-linked and bundled actin filaments are ubiquitous in the cellular cytoskeleton, but their elasticity remains poorly understood. We show that these networks exhibit exceptional elastic behavior that reflects the mechanical properties of individual filaments. There are two distinct regimes of elasticity, one reflecting bending of single filaments and a second reflecting stretching of entropic fluctuations of filament length. The mechanical stiffness can vary by several decades with small changes in cross-link concentration, and can increase markedly upon application of external stress. We parameterize the full range of behavior in a state diagram and elucidate its origin with a robust model.

Stress-Dependent Elasticity of Composite Actin Networks as a Model for Cell Behavior

“…Ultimately the network ruptures and G 0 0:5 decreases dramatically; this occurs at a stress, max 3 Pa, and strain, max 50%. This transition between stress weakening and stress stiffening in cross-linked networks is consistent with previous results for cross-linked F-actin networks [8,13].…”

“…The stress-stiffening behavior of these networks is roughly 20-fold larger than any previously reported [5,8,9]. Furthermore, in contrast to covalently cross-linked F-actin networks, c and the maximum strain of the linear regime of these networks are both rather insensitive to changes in R [13]. Instead, the parameter that is most sensitive to variations in R is max ; these networks can withstand stresses 10 -100 times larger than G 0 .…”

“…The magnitude of G 0 is remarkably insensitive to further increases in R, as shown in the inset to Fig. 1; this is in sharp contrast to F-actin networks formed with rigid cross-links, where G 0 increases significantly, varying as G 0 R 3 [13]. Moreover, the dissipation is significant as G 00 remains comparable to G 0 as the FLNa concentration is increased; this also contrasts sharply with rigidly crosslinked F-actin networks, where the relative magnitude of G 00 to G 0 decreases with increased R [12].…”

“…The utility of this in vitro model system is that it greatly facilitates understanding the underlying mechanical behavior of these composite FLNa-F-actin networks which is qualitatively different from other F-actin networks [13]. In the linear regime, the mechanical stiffness is fairly insensitive to large variations in the concentration of FLNa cross-links.…”

“…However, the rheological properties of in vitro F-actin networks are quite different from those of cells: the magnitude of the elastic modulus typically underestimates that measured in cells, often by several orders of magnitude. In addition, unlike the linear behavior assumed for cells [1][2][3]10], the viscoelasticity of F-actin networks is linear only for very small deformations; like most semiflexible biopolymers [11], it rapidly becomes strongly nonlinear with increasing deformation [5,9,12,13]. One possible cause for this discrepancy is the fact that, in vivo, F-actin is cross-linked with a variety of actin-binding proteins (ABP's), which are essential in determining the elastic properties of the cytoskeleton.…”