Tuning Synthetic Semiflexible Networks by Bending Stiffness

The mechanics of complex soft matter often cannot be understood in the classical physical frame of flexible polymers or rigid rods. The underlying constituents are semiflexible polymers, whose finite bending stiffness ($\kappa$) leads to nontrivial mechanical responses. A natural model for such polymers is the protein actin. Experimental studies of actin networks, however, are limited since the persistence length ($l_p\propto \kappa$) cannot be tuned. Here, we experimentally characterize this parameter for the first time in entangled networks formed by synthetically produced, structurally tunable DNA nanotubes. This material enabled the validation of characteristics inherent to semiflexible polymers and networks thereof, i.e., persistence length, inextensibility, reptation, and mesh size scaling. While the scaling of the elastic plateau modulus with concentration $G_0\propto c^{7/5}$ is consistent with previous measurements and established theories, the emerging persistence length scaling $G_0\propto l_p$ opposes predominant theoretical predictions.

Figure 1

$n$-helix tube ($n\mathrm{HT}$) filament architecture. (a) Schematic of the assembly of a 4HT formed of four distinct 42-mers. Adjacent single-stranded DNA oligonucleotides share continuous complementary sections of 10 and 11 bases in length (long black ticks). Boundary strands U1 and T4 feature complementary sequences as well, enabling the formation of a tubelike ring from the planar sheet structure. The half-staggered motif of these rings with sticky ends on both sides promotes polymerizationlike axial growth. (b) Cross sections of all seven different $n\mathrm{HTs}$ employed in this study with according measured values for $l_p$. Strand numbers range from 4 to 14HT and $l_p$ from 1.2 to $26\mu \mathrm{m}$, respectively. (c),(d) Epifluorescent image of Cy3-labeled adsorbed $n\mathrm{HTs}$. Left: 5HT. Right: 10HT. The red overlay is the filament contour approximated by image analysis with end-to-end distance $R$ and contour length $l_c$ [33]. (a)and (b) Inspired by Yin et al. [21].

Figure 2

Network elasticity. (a) Schematic of a semiflexible filament meshwork with mesh size $\xi$. A test polymer (blue) of contour length $l_c$ is confined by the background of red filaments to a tube of width $a$. (b) AFM image of an 8HT network formed at $4\mu \mathrm{M}$. (c) Frequency resolved viscoelastic properties of an 8HT network at $6\mu \mathrm{M}$ probed by bulk shear rheology at a strain of 5%. A pronounced elastic rubber plateau over more than 4 orders of magnitude is characteristic of all $n\mathrm{HTs}$.

Figure 3

$G_0$ scaling of $n\mathrm{HT}$ networks. (a) The concentration scaling for networks of different $n\mathrm{HT}$ is plotted. Predicted power laws from the tube model and unit cell approach are given by black and dashed lines, respectively. (b) Least-squares approximations yielded the actual power law exponents for all $n\mathrm{HT}$, which accumulated around $\alpha \approx 7/5$. (c) The persistence length scaling for networks of different concentration is shown. (d) Approximated power law exponents yielded a mean exponent of $\beta \approx 1$. In summary, we found the elastic shear modulus to scale as $G_0\propto c^{7/5}{l}_p$.

Figure 4

Linearity and microscopic mesh size. (a) Strain sweeps of $G^{\prime }(1\mathrm{Hz})$ feature a broad linear elastic plateau for small strains. Beyond a characteristic strain $G^{\prime }$ breaks off irreversibly depending on $n\mathrm{HT}$. (b) Microscopic reptation of a single labeled DNA 8HT embedded in a network of the same type of filaments. The summation fluorescent image of 600 sampled configurations is overlaid by three exemplary filaments as found by image analysis ($c=14\mu \mathrm{M}$). Inset: Mesh size of actin and DNA 8HT networks as derived from such reptation analysis at different concentrations. Monomeric concentrations are shifted by the chain length conversion factor $x=l_{\text{monomer},n\mathrm{HT}}/l_{\text{monomer},\text{actin}}\simeq 2.5$ to compare the same concentrations of contour length per unit volume. Mesh sizes are on the same order of magnitude and decrease with concentration. Theoretical scaling prediction $\xi \propto c^{-1/2}$ is indicated by the solid line [35].