Multiscale mechanics and temporal evolution of vimentin intermediate filament networks

Abstract

The cytoskeleton, an intricate network of protein filaments, motor proteins, and cross-linkers, largely determines the mechanical properties of cells. Among the three filamentous components, F-actin, microtubules, and intermediate filaments (IFs), the IF network is by far the most extensible and resilient to stress. We present a multiscale approach to disentangle the three main contributions to vimentin IF network mechanics-single-filament mechanics, filament length, and interactions between filaments-including their temporal evolution. Combining particle tracking, quadruple optical trapping, and computational modeling, we derive quantitative information on the strength and kinetics of filament interactions. Specifically, we find that hydrophobic contributions to network mechanics enter mostly via filament-elongation kinetics, whereas electrostatics have a direct influence on filament-filament interactions.

Keywords: cytoskeleton; intermediate filaments; microrheology; network mechanics; quadruple optical tweezers.

Fig. 1.

Formation and mechanics of vimentin networks. (A) Microscopy images of vimentin networks after 3 d (74 to 80 h) of network-formation time, with buffer conditions indicated below each image. A, Insets show representative tracks from MPT, recorded over the course of 6 min after 3 d (71 h) of network formation. (B) Median MSD for each condition for increasing network-formation times (for color code, see legend); the particle diameter $a$ = 2 $\mathrm{\mu }$m is indicated by arrows. Individual curves are shown in SI Appendix, Figs. S5–S7. (C) Elongation of the filaments; shown is the length average $l_M$. The corresponding cumulative length histograms from three interdependent datasets are provided in SI Appendix, Fig. S3, and the extent of reaction $q$ as determined from step-growth polymerization is shown in SI Appendix, Fig. S4. (D) Comparison of active (symbols) and passive (lines) microrheology measurements after 3 d. The error bars denote the SD of the active measurements. (E) Temporal evolution of $G^{\prime }$ at $\omega =$ 1 ${\mathrm{s}}^{-1}$. (F) Temporal evolution of the relaxation times of single filaments in the network. (G) Temporal evolution of the bundling parameters, calculated from the shift of $G″=b{\omega }^{3/4}-\eta \omega$ (12) at high frequencies. For C, E, F, and G, the median values of the results, analyzed sample by sample, are shown, along with the minimum and maximum, indicated by the error bars. For each time point and condition, between one and five samples are measured; see SI Appendix, Figs. S5–S7 for the numbers of samples and particles. (H) Schematic of the filament and network-formation process with the competition between lateral assembly—i.e., bundling—and filament elongation that leads to an entangled network.

Fig. 2.

Interaction measurements. (A) Confocal image series of a filament pair showing deformation of the horizontal filament as a consequence of the interaction and the return to the initial conformation after rupture of the interaction. (B) Schematic of the measuring geometry and nomenclature used in the experiments. We measure and analyze the force $F_{1y}$ acting on b1 (green). (C) Typical interaction force, $F$, plotted against time for the filament pair shown in A; rupture force $F_i$. (D) Typical force–time curve for a measurement with interaction, rupture of the interaction with rebinding under force, and rupture of the interaction. (E) Force–time curve for a strong interaction of filaments that show “zipping,” as shown in the micrograph in F.

Fig. 3.

Results of the interaction experiments and simulation. (A) Histograms of the rupture forces from experiments (colored bars) and mean curve of the simulation results (black) with SD (shaded area). With decreasing TX concentration (red, orange, and yellow), higher forces are reached. The addition of ${\mathrm{M}\mathrm{g}}^{2+}$ (green, blue, and purple) causes a broadening of the force distribution and a shift toward higher forces. (B) Force-independent binding rate $r_{e,b}$. The binding rate is constant, unless ${\mathrm{M}\mathrm{g}}^{2+}$ is present at a concentration of 20 mM. The mean and SD are determined from bootstrap resampling of all single measurements. (C) Schematic of the two-state model used for the simulations. (D) Parameter pairs of $x_u$ and the force-independent unbinding rate $r_{e,u}$, extracted from the simulation, that satisfy the 5$\%$ significance level in the Kolmogorov–Smirnov test. The centroid of each parameter space is marked. (E and F) Energy landscapes corresponding to the centroid of the parameter space. The relative $E_A$ values are shown. The ordinate axis is interrupted to indicate the unknown absolute height of the transition state.