Synergistic Interactions Between DNA and Actin Trigger Emergent Viscoelastic Behavior

Abstract

Composites of flexible and rigid polymers are ubiquitous in biology and industry alike, yet the physical principles determining their mechanical properties are far from understood. Here, we couple force spectroscopy with large-scale Brownian Dynamics simulations to elucidate the unique viscoelastic properties of custom-engineered blends of entangled flexible DNA molecules and semiflexible actin filaments. We show that composites exhibit enhanced stress-stiffening and prolonged mechano-memory compared to systems of actin or DNA alone, and that these nonlinear features display a surprising nonmonotonic dependence on the fraction of actin in the composite. Simulations reveal that these counterintuitive results arise from synergistic microscale interactions between the two biopolymers. Namely, DNA entropically drives actin filaments to form bundles that stiffen the network but reduce the entanglement density, while a uniform well-connected actin network is required to reinforce the DNA network against yielding and flow. The competition between bundling and connectivity triggers an unexpected stress response that leads equal mass DNA-actin composites to exhibit the most pronounced stress-stiffening and the most long-lived entanglements.Mixing polymers with distinct structural features and stiffnesses endows composite materials with unique macroscopic properties such as high strength and resilience coupled with low weight and malleability [1][2][3][4]. These versatile materials, ranging from carbon nanotube-polymer nanocomposites and liquid crystals to cytoskeleton and mucus, have numerous applications from tissue engineering to high-performance energystorage [2,[5][6][7][8][9][10][11][12]. Compared to single-constituent materials, polymer composites offer a wider dynamic range and increased control over mechanical properties by tuning the relative concentrations and properties of the different species. Importantly, the unique mechanics that emerge in composites often cannot be deduced from those of the corresponding single-component systems [3,[13][14][15][16][17]. However, the physical principles that couple structural interactions to mechanics in composites remain elusive.Over the past two decades, DNA and actin have been extensively studied as model polymer systems [18][19][20][21][22]. While the contour lengths of each biopolymer can be comparable (L≈10-50 µm), actin is much stiffer than DNA with a persistence length lp of ~10 µm compared to lp≈50 nm for DNA. When sufficiently long, both polymers form entangled networks over similar concentrations (c≈0.1-2.5 mg/ml), with actin forming nematic domains above 2.5 mg/ml [18]. Despite their wide use as model systems, very few studies have examined composites of actin and DNA, focusing solely on steady-state structure at concentrations above the nematic crossover or under microscale confinement [23][24][25]. These studies reported large-scale phase separation such that DNA and actin polymers were rarely interacting. Co-entangled systems of DNA and actin have yet to be i...

Maximally stiffening composites require maximally coupled rather than maximally entangled polymer species

“…For pure solutions of short DNA (φ A = 0, L DN A = 3.67 µm, Z DN A 1) we observe G(t) ∼ t −1/2 , in agreement with the Rouse behaviour of poorly entangled chains [43], whereas we find G(t) ∼ t −1/3 for longer DNAs, in agreement with previously reported values for =0.75 =0.5 =0.25 entangled DNA [23,32]. Conversely, pure actin networks (φ A = 1) display an initial decay of G(t) ∼ t −1 , in between t −2/3 and t −5/4 predicted in Ref.…”

“…We choose a coarse-grain level at which each polymer bead is 25 nm, equivalent to half the DNA persistence length and 9.2 actin monomers (see Materials and Methods). Similar coarse-grained models for DNA and actin have been employed in the literature [32,40] and have been shown to well capture the dynamics of experimental systems.…”

“…As described in the Introduction, we choose to fix the overall concentration of our composites to c = 0.8 mg/ml at which the entanglement tube diameter a and entan-glement time τ e for solutions of only DNA or actin are matched [32]. This allows us to tune the relative concentrations of flexible polymers (DNA, l p 50 nm) and semiflexible ones (actin, l p 10 µm), as well as the length of the flexible component, while preserving key polymer physics quantities.…”

“…These studies have shed important light on our understanding of entangled polymers and the tube models used to describe them [26][27][28][29]. Yet, there is limited knowledge on how composites of these two iconic biopolymers behave [30][31][32]. Here, we tackle the vast multi-dimensional parameter space of our previously introduced custom-engineered actin-DNA composites to elucidate the role that DNA length, number of entanglements, and dynamics play in their emergent rheological properties.…”

“…Importantly, we recently discovered that these composites exhibit unique viscoelastic properties that depend non-monotonically on the actin fraction φ A [32]. Yet, how their mechanical behaviour depends on the myriad of other tunable system parameters, such as polymer length and number of entanglements, remains unknown.…”