Co-Entangled Actin-Microtubule Composites Exhibit Tunable Stiffness and Power-Law Stress Relaxation

Abstract

We use optical tweezers microrheology and fluorescence microscopy to characterize the nonlinear mesoscale mechanics and mobility of in vitro co-entangled actin-microtubule composites. We create a suite of randomly oriented, well-mixed networks of actin and microtubules by co-polymerizing varying ratios of actin and tubulin in situ. To perturb each composite far from equilibrium, we use optical tweezers to displace an embedded microsphere a distance greater than the lengths of the filaments at a speed much faster than their intrinsic relaxation rates. We simultaneously measure the force the filaments exert on the bead and the subsequent force relaxation. We find that the presence of a large fraction of microtubules (>0.7) is needed to substantially increase the measured force, which is accompanied by large heterogeneities in force response. Actin minimizes these heterogeneities by reducing the mesh size of the composites and supporting microtubules against buckling. Composites also undergo a sharp transition from strain softening to stiffening when the fraction of microtubules (ϕ) exceeds 0.5, which we show arises from faster poroelastic relaxation and suppressed actin bending fluctuations. The force after bead displacement relaxes via power-law decay after an initial period of minimal relaxation. The short-time relaxation profiles (t < 0.06 s) arise from poroelastic and bending contributions, whereas the long-time power-law relaxation is indicative of filaments reptating out of deformed entanglement constraints. The scaling exponents for the long-time relaxation exhibit a nonmonotonic dependence on ϕ, reaching a maximum for equimolar composites (ϕ = 0.5), suggesting that reptation is fastest in ϕ = 0.5 composites. Corresponding mobility measurements of steady-state actin and microtubules show that both filaments are indeed the most mobile in ϕ = 0.5 composites. This nonmonotonic dependence of mobility on ϕ demonstrates the important interplay between mesh size and filament rigidity in polymer networks and highlights the surprising emergent properties that can arise in composites.

Varying crosslinking motifs drive the mesoscale mechanics of actin-microtubule composites

“…To systematically investigate the role that crosslinking plays in composites of actin and microtubules we design actin-microtubule composites with four distinct crosslinking motifs. We use our previously established protocols 27 to create equimolar co-entangled actin-microtubule composites. We then incorporate biotin-NeutrAvidin complexes into composites to selectively crosslink the filamentous proteins, keeping the crosslinker:protein ratio fixed at R = 0.02 37 .…”

“…Most biopolymer networks, including entangled actin-microtubule composites, display viscoelastic behavior in between these two extremes. 2,27 However, crosslinking can lead to more elastic response by suppressing network rearrangements and polymer bending modes that can dissipate stress 11,37 . Figure 2b shows that Class 2 composites exhibit nearly complete elastic response while Class 1 exhibits softening and yielding to viscous behavior.…”

“…As described above, elastic and viscous systems should display starkly different relaxation behaviors following strain, with purely elastic systems exhibiting no relaxation and viscous systems exhibiting immediate and complete force relaxation. Viscoelastic systems display behavior in between these two extremes, with viscoelastic biopolymer networks exhibiting both exponential and power-law relaxation over varying timescales 2,27,[36][37][38]63 . To characterize the relaxation dynamics of the composites, we measure the time-dependent force F(t) exerted on the bead by each composite for 15 s following the strain (Figs.…”

“…Aside from the obvious physiological relevance, investigations of actin-microtubule composites with variable crosslinking motifs are motivated by materials engineering, as they serve as a model platform for designing and investigating flexible-stiff polymer composites 2,11,26,27 . In order to increase stiffness, strength, and toughness in composite materials, soft polymer networks are often reinforced with stiffer, load bearing fibers such as nanotubes and carbon nanofibers 11,26,28,29 .…”

“…Few studies have investigated composite networks of actin and microtubules 11,27,57,58 due, in part, to the incompatibility of standard polymerization conditions for each protein 27 . However, methods have recently been introduced to co-polymerize actin and tubulin in situ to create randomly-oriented co-entangled composites of actin and microtubules 27 . The first study that employed these methods used microrheology and microscopy techniques to show that a surprisingly large molar fraction of microtubules (>70%) was needed to substantially increase the response force of the composites.…”