Reversible stress softening of actin networks

Abstract

The mechanical properties of cells play an essential role in numerous physiological processes. Organized networks of semiflexible actin filaments determine cell stiffness and transmit force during mechanotransduction, cytokinesis, cell motility and other cellular shape changes. Although numerous actin-binding proteins have been identified that organize networks, the mechanical properties of actin networks with physiological architectures and concentrations have been difficult to measure quantitatively. Studies of mechanical properties in vitro have found that crosslinked networks of actin filaments formed in solution exhibit stress stiffening arising from the entropic elasticity of individual filaments or crosslinkers resisting extension. Here we report reversible stress-softening behaviour in actin networks reconstituted in vitro that suggests a critical role for filaments resisting compression. Using a modified atomic force microscope to probe dendritic actin networks (like those formed in the lamellipodia of motile cells), we observe stress stiffening followed by a regime of reversible stress softening at higher loads. This softening behaviour can be explained by elastic buckling of individual filaments under compression that avoids catastrophic fracture of the network. The observation of both stress stiffening and softening suggests a complex interplay between entropic and enthalpic elasticity in determining the mechanical properties of actin networks.

Figure 1. AFM-based microrheology of growing dendritic actin networks

a, Cartoon illustrating the measurement geometry in which the surface is driven sinusoidally (blue sinusoid and double-headed arrow), and the force transmitted through the network (red mesh) is transduced by the cantilever (pink sinusoid and double-headed arrow). b, Fluorescence micrograph of the actin network, which is used to calculate the network area A. Scale bar is 10 µm. c, Graph showing surface drive and cantilever response signal as a function of time for a 5 Hz measurement (colours are as in a). Note the cantilever response is damped with respect to the drive signal indicating compression of the network. This technique has the effect of applying a sinusoidal stress on the network where hydrodynamic coupling was found to be negligible (see Supplementary Information B). d, Stress and strain graph calculated from measurement in c showing stress (black) and strain (red) as a function of time (see Methods).

Figure 2. Frequency dependence of elastic (filled triangles, E′) and viscous (open triangles, E″) moduli

The traces were constructed by averaging normalized data from 11 separate experiments and 21 different frequency sweeps. Each measurement of the elastic and viscous moduli was normalized by the average elastic modulus at 5 Hz taken before and after the measurement (see Supplementary Information C). The best-fit power-law exponent for E′(f) was determined to be x = 0.13 (dotted line), and the average elastic modulus at 5 Hz was 985 ± 655 Pa (mean ± s.d.), which are consistent with previous studies on cells. In addition to the power-law behaviour, the viscous modulus has a similar shape to those seen previously. Error bars on both curves are normalized s.d.

Figure 3. Dendritic actin networks exhibit stress stiffening and reversible stress softening

a, In a typical nonlinear elasticity measurement, the stress on the network is first increased incrementally (black trace) to and then decreased incrementally from a maximum stress (red trace) of ~600 Pa, with the elasticity measured at each stress at 5 Hz. The elasticity remains constant for stresses up to ~15 Pa and then increases in a stress-stiffening regime. For stresses above the critical stress σ_c of ~270 Pa, the elasticity decreases in a stress-softening regime that is reversible, as indicated by the overlay of the black and red traces. b, Averaged and normalized trace of the nonlinear elasticity of actin networks (see Supplementary Information A). Each individual measurement was normalized by the difference between the elasticity before the measurement E_min and the maximum elasticity for increasing stresses E_max and σ_c. The results of 28 different measurements from 12 separate experiments were averaged together (mean ± s.d. shown) and found to exhibit three distinct regimes of elasticity: linear, stress stiffening and stress softening. The stress softening is shown to be reversible. Note that the elasticity in b is shown on a linear scale while the elasticity in a is shown on a log scale. The inset shows a histogram of σ_c for which the mean value was 233 Pa.

Figure 4. Stress stiffening and stress softening can arise in dendritic networks owing to filaments resisting extension and buckling of filaments resisting compression

a, b, When the stress on the network (σ, indicated by black arrows) is increased from σ = 0, a population of filaments or crosslinkers is stretched (as indicated by green arrows) as the material expands laterally, and the resistance to extension of filaments increases owing to entropic elasticity, leading to a stress-stiffening regime. c, However, as the stress is increased above σ_c, some filaments resisting compression buckle when the compressional force (green arrows) exceeds the Euler buckling force. Buckled filaments exhibit infinite compliance, so they no longer contribute to the elasticity, but they do not collapse because they have connections with the network and thus still support the buckling force. d, As the stress is further increased, more filaments buckle and the elasticity of the network is decreased further, leading to the stress-softening regime. In principle, this process is completely reversible because buckled filaments will unbuckle once the stress is reduced.