Emergent properties of composite semiflexible biopolymer networks

Abstract

The semiflexible polymers filamentous actin (F-actin) and intermediate filaments (IF) both form complex networks within the cell, and together are key determinants of cellular stiffness. While the mechanics of F-actin networks together with stiff microtubules have been characterized, the interplay between F-actin and IF networks is largely unknown, necessitating the study of composite networks using mixtures of semiflexible biopolymers. We employ bulk rheology in a simplified in vitro system to uncover the fundamental mechanical interactions between networks of the 2 semiflexible polymers, F-actin and vimentin IF. Surprisingly, co-polymerization of actin and vimentin can produce composite networks either stronger or weaker than pure F-actin networks. We show that this effect occurs through steric constraints imposed by IF on F-actin during network formation and filament crosslinking, highlighting novel emergent behavior in composite semiflexible networks.

Keywords: F-actin, filamentous actin; G-actin, globular (monomeric) actin; IF, intermediate filament; actin; composite; intermediate filaments; model systems; networks; rheology; semiflexible polymers; vimentin.

Figure 1.

Stress‑strain curves of composite F‑actin‑vimentin IF networks with a ratio of 1:100 biotinylated actin to plain actin. Samples exhibit an initial elasticity ${\displaystyle G\prime =\text{Δ}\sigma /\text{Δγ}}$ before undergoing strain stiffening at a critical strain ${\displaystyle {\gamma }_{crit}}$, evident as an increase in the tangent modulus ${\displaystyle K\prime =\partial \sigma /\partial \gamma }$ (the slope of the stress‑strain curve). The peak of the curve indicates the yield stress ${\displaystyle {\sigma }_{max}}$, the maximal stress the network can withstand before failing. (A) At actin concentrations of 18 ${\displaystyle \text{μM}}$, the maximal stress is decreased as the vimentin concentration is increased from 0 ${\displaystyle \text{μM}}$ (light gray) through 0.3 ${\displaystyle \text{μM}}$ and 1.5 ${\displaystyle \text{μM}}$ to 3 ${\displaystyle \text{μM}}$ (black). (B) In contrast, the addition of vimentin, from 0 ${\displaystyle \text{μM}}$ through 0.3 ${\displaystyle \text{μM}}$ and 1.5 ${\displaystyle \text{μM}}$ to 3 ${\displaystyle \text{μM}}$, increases the yield stress of the composite network at actin concentrations of 6 ${\displaystyle \text{μM}}$.

Figure 2.

Co‑polymerization with vimentin strengthens F-actin networks at low actin concentrations, but weakens networks at high actin concentrations. (A) Fractional change in yield stress ${\displaystyle {\sigma }_{max}}$ as a function of actin and vimentin concentrations. Increasing the actin concentration gradually reduces the increase in yield stress and transitions to a reduction in yield stress at sufficiently high actin concentrations. (B) Absolute change in linear elastic modulus ${\displaystyle G\text{'}}$ of F-actin-vimentin IF composite networks compared to vimentin‑free networks. At low actin concentrations, vimentin IF adds roughly linearly to ${\displaystyle G\text{'}}$. At higher actin concentrations, vimentin IF contributes less to the elasticity, and can even result in a decrease of composite network elasticity. (C) Fractional change in the maximal nonlinear elasticity ${\displaystyle K{\text{'}}_{max}}$ exhibited by the composite networks under strain. At low actin concentrations, vimentin IF adds to the nonlinear elasticity of the networks, while the nonlinear elasticity is reduced with vimentin IF at high actin concentrations. All values are measured relative to vimentin‑free F‑actin networks at a given actin concentration.

Figure 3.

Vimentin strengthening or weakening of F-actin networks is dependent on the density of F‑actin crosslinkers. In a 15 ${\displaystyle \text{μM}}$ F‑actin network, at high crosslinking densities (small average distance between crosslinkers), co‑polymerization with 3 ${\displaystyle \text{μM}}$ vimentin increases the maximal composite network stress and linear elastic modulus, while lowering the critical strain of composite network strain stiffening. The opposite trend is seen at lower crosslinking densities (larger average distance between crosslinkers), as 3 ${\displaystyle \text{μM}}$ vimentin delays the onset of strain stiffening, but decreases the linear elastic modulus and maximal composite network stress. All fractional changes are measured relative to a vimentin‑free 15 ${\displaystyle \text{μM}}$ F-actin network.

Figure 4.

Illustration of the approximate F-actin‑vimentin IF network geometry for an actin concentration of 15 ${\displaystyle \text{μM}}$ and a vimentin concentration of 3 ${\displaystyle \text{μM}}$. Actin filaments are bound to each other through biotin‑neutravidin crosslinks, while vimentin IF are crosslinked by magnesium. The result is an interpenetrating network of the 2 species of biopolymers. At a 1:100 actin biotinylation ratio, the average distance between actin crosslinking sites is comparable to the actin network mesh size.

Figure 5.

Vimentin IF restricts F-actin fluctuations, which leads to a loss of F‑actin crosslinking when F‑actin crosslinkers are scarce. Shaded areas indicate the volume explored by an actin filament through thermal fluctuations before these are reduced by crosslinking. (A) When F‑actin crosslinkers are abundant, several biotins are within reach of a given biotin‑neutravidin site, indicated by stars, and any of these can bind to crosslink the 2 actin filaments. (B) Co‑polymerization with vimentin to form IF constrains actin filament fluctuations, but biotin sites are still within reach at high biotin densities, and an F‑actin crosslink can form. (C) At low biotin densities, reachable crosslinking partners are fewer and farther apart. (D) Steric constraints by vimentin IF can now result in a loss of F‑actin crosslinking, weakening the resulting composite network.