Prestressed F-actin networks cross-linked by hinged filamins replicate mechanical properties of cells

Abstract

We show that actin filaments, shortened to physiological lengths by gelsolin and cross-linked with recombinant human filamins (FLNs), exhibit dynamic elastic properties similar to those reported for live cells. To achieve elasticity values of comparable magnitude to those of cells, the in vitro network must be subjected to external prestress, which directly controls network elasticity. A molecular requirement for the strain-related behavior at physiological conditions is a flexible hinge found in FLNa and some FLNb molecules. Basic physical properties of the in vitro filamin-F-actin network replicate the essential mechanical properties of living cells. This physical behavior could accommodate passive deformation and internal organelle trafficking at low strains yet resist externally or internally generated high shear forces.

Fig. 1.

The stress–strain relationships of F-actin networks formed with different FLN mutants. (A) A schematic of the hinged and hingeless isoforms of filamin. The filamin molecule is homodimer; each monomer consists of an actin binding domain (rectangles at top), 24 β-sheet repeats (squares), and two unstructured, amino acid sequences between the 15th and 16th repeats and 23rd and 24th repeats (black lines) that serve as flexible hinges. Dimerization occurs at the 24th repeat. The hingeless mutants we study, FLNa h(−) and FLNb h(−), lack the hinge region between the 15th and 16th repeats. (B) The relationship between the stress and the strain at an oscillatory frequency of 0.5 Hz for 48 μM F-actin with 0.12 μM gelsolin cross-linked with 0.48 μM FLNa (filled squares), FLNb (filled triangles), FLNb h(−) (open triangles), and FLNa h(−) (open squares). The stress–strain is approximately linear at all values of stress below 0.5 Pa. In the networks cross-linked with FLNa and FLNb, the stress diverges at stresses above 0.5 Pa and the networks catastrophically break at stresses of 30 Pa and 10 Pa, respectively. In contrast, the networks formed with FLNa h(−) and FLNb h(−) disintegrate at stresses larger than 0.1 Pa and weaken at large strains. (C) A schematic illustration examining the implications of the nonlinearity in the stress–strain relationship. In the linear elastic regime of a material, the relationship between the force per unit area, or stress (ς), and its resulting deformation, or strain (γ), is a simple, linear relationship: ς = G′γ, where G′ is the elastic spring constant. Thus the ratio ς/γ will measure the same spring constant as measuring the differential spring constant, dς/dγ, at a given extension. Typically, materials exhibit linear elasticity over a range of stresses and strains. At larger stresses, nonlinear effects can start to dominate the response. In the nonlinear regime, the relationship between ς and γ is nonlinear and, thus, ς/γ (the slope indicated by the dashed line) will measure a different spring constant than a differential measurement, dς/dγ, (slope indicated by the dotted line) at a fixed stress. Thus, for a nonlinear spring, there are different measures of its spring constant.

Fig. 2.

The linear mechanical properties of 48μM F-actin network, where filament length is regulated with 0.12 μM gelsolin and cross-linked with 0.48 μM FLNa. Insets schematize the mechanical tests performed. (A) Creep test. We apply a constant stress, or force per unit area (Inset, filled arrow), of 0.03 Pa for 150 sec and measure the resultant displacement (Inset, dashed arrow) over this time. The strain, γ, is the ratio of the plate displacement to the plate separation. The strain slowly evolves with time, increasing from 0.02 to 0.08 over 150 sec, and evolves as a power law such that γ ∼ t^x where x = 0.17 (Fig. 4). Upon removal of the stress, the strain recovers to nearly zero following a power law, γ ∼ t^γ, with γ ≈ 0.17. (B) The dynamic elastic and viscous loss moduli, G′ (filled squares) and G″ (open squares), are determined by measuring the resulting deformation (Inset, dashed arrow) to an applied oscillatory stress (Inset, filled arrow) as a function of frequency. We apply a sufficiently small stress, 0.01 Pa, to stay within the linear elastic regime of the network. A prestress of 15 Pa is applied to this network, and we superpose a small, linear oscillatory stress to measure the differential elastic and loss moduli, K′ (filled triangles) and K″ (open triangles).

Fig. 3.

We apply a prestress, ς₀, to the network (Inset, single-headed filled arrow) and measure the deformation (Inset, dashed arrow) in response to an additional oscillatory stress (Inset, double-headed filled arrow). We measure the differential elastic stiffness, K′, at 0.2 Hz over a range of concentrations of actin, c_A, and molar ratio of FLNa, R: c_A = 36 μM, R = 1/100 (open squares), c_A = 48μM, R = 1/100 (filled squares), c_A = 74 μM, R = 1/100 (diamonds), c_A = 36 μM, R = 1/50 (left-pointing triangles), and c_A = 53μM, R = 1/50 (upward-pointing triangles). All of the networks have the identical differential stiffness for a given prestress. However, differences between these networks are seen at the maximum stress they can withstand before breaking; the maximum prestress of several networks is indicated by the filled arrows; thus, differences in total protein concentration affect the maximum stress the network can withstand. Under identical network conditions, the hingeless mutants do not exhibit such stress stiffening (open circles); rather, at stresses beyond the linear elastic regime, these networks disintegrate. In vivo measurements where the prestress of the cell is correlated to its stiffness, as measured with twisting bead cytometry from ref. , are indicated by the black stars. Thus, there is quantitative comparison between our in vitro measurements of prestressed FLNa–F-actin networks with in vivo measurements of adherent cells.