Cytoskeletal polymer networks: the molecular structure of cross-linkers determines macroscopic properties

Abstract

In living cells the mechanical properties of the actin cytoskeleton are defined by the local activation of different actin cross-linking proteins. These proteins consist of actin-binding domains that are separated and geometrically organized by different numbers of rod domains. The detailed molecular structure of the cross-linking molecules determines the structural and mechanical properties of actin networks in vivo. In this study, we systematically investigate the impact of the length of the spacing unit between two actin-binding domains on in vitro actin networks. Such synthetic cross-linkers reveal that the shorter the constructs are, the greater the elastic modulus changes in the linear response regime. Because the same binding domains are used in all constructs, only the differences in the number of rod domains determine their mechanical effectiveness. Structural rearrangements of the networks show that bundling propensity is highest for the shortest construct. The nonlinear mechanical response is affected by the molecular structure of the cross-linker molecules, and the observed critical strains and fracture stress increase proportional to the length of the spacing unit.

Fig. 1.

Transmission electron microscopy images of cross-linked actin networks (c_A = 9.5 μM, mean filament length 〈l_FA〉 = 21 μm, and R = 0.1). (A) Actin without cross-linker. (C and D) HisAc-S-S-HisAc. (E) HisAc-D5-6. (B and F) HisAc-D2-6. (G) ddFLN cross-linked actin. Whereas for HisAc-S-S-HisAc the bundles appear straight and compact (C and D), bundles observed in ddFLN or HisAc-D2-6 cross-linked networks are significantly more curved (F and G) and appear less dense (B, white arrows indicate the cross-linkers). (Magnification: A and D–G, ×2,950; B and C, ×28,500.)

Fig. 2.

G′(f) (filled symbols) and G″(f) (open symbols) of cross-linked actin networks measured in bulk with a rotating-disk rheometer at c_A = 9.5 μM and 〈l_FA〉 = 21 μm at different molar ratios, R. (A) HisAc-S-S-HisAc. (B) HisAc-D5-6. (C) HisAc-D2-6. (D) ddFLN. For all cross-linker molecules, the different concentration ratios, R, shown are R = 0 (actin; filled triangles and open inverted triangles), R = 1 (filled and open orange hexagons), R = 0.5 (filled and open stars), R = 0.1 (filled and open squares), R = 0.04 (filled and open green circles), and R = 0.02 (filled and open diamonds). All frequency sweeps show a flattening of G′ and a shift in the crossover frequency with increasing R. (A Inset–D Inset) Schematics of the cross-linker constructs from structural data of single domains.

Fig. 3.

Plateau modulus G₀ depends on R at c_A = 9.5 μM with 〈l_FA〉 = 21 μm for HisAc-S-S-HisAc (circles), HisAc-D5-6 (stars), HisAc-D2-6 (squares), and ddFLN (diamonds) cross-linked actin networks. Above a critical ratio R*, G₀ increases in all cross-linked networks as G₀ ≈ (R)^x with x = 1.2 (HisAc-S-S-HisAc), x = 0.6 (HisAc-D5–6), x = 0.5 (HisAc-D2-6), and x = 0.4 (ddFLN). (Inset) The dependence of the scaling exponent x (squares) and R* (bars) with cross-linker MW. The error bars were obtained by assuming different threshold values R* (Materials and Methods).

Fig. 4.

The recorded stress (τ) and strain (γ) dependence of F-actin networks (c_A = 9.5 μM with 〈l_FA〉 = 21 μm) with HisAc-S-S-HisAc (circles), HisAc-D5-6 (stars), HisAc-D2-6 (squares), and ddFLN (diamonds) cross-linkers at a constant R = 0.1. Arrows pointing left illustrate the maximal reachable stress τ_max, and downward-facing arrows indicate the onset of the nonlinearity γ_crit. (Inset) γ_crit (circles) and τ_max (squares) are shown over the MW of the cross-linking constructs. The dotted line indicates a linear relation.