# Mechanical Properties of DNA Hydrogels: Towards Highly Programmable Biomaterials
## 2 Structural DNA Hydrogel Design
### Nanostructured  
Nanostructured DNA hydrogels are most commonly constructed from multivalent DNA nanostars (DNAns) (Figure 1c) [50; 61; 62; 63]. Alternatively, short multidomain self-assembling strands have been used to construct complementary linear sections of dsDNA crosslinked by complementary overhangs (Figure 1d) [64; 65]. [PERSON] et al. designed a single short DNA strand with 3-6 self-complementary binding domains of 12-20 nt in length to form a DNA hydrogel. The rheological characterization of 2% \(w/v\) DNA hydrogels formed from strands with 3, 4, 5, and 6 domains of 12 nt in length showed a storage modulus of \(\sim\)3000, 1000, 7, and 7 Pa, respectively. Interestingly, when the 3 domain strand was tested with different length domains, 12, 16, 20 nt, a storage modulus of \(\sim\)3000, 10, and 80 Pa was observed respectively [64]. This approach yielded counterintuitive results where an increase in valency and hybridization interaction yielded lower storage moduli, which demonstrates the need to consider the availability of binding sites in nanostructured designs. [PERSON] et al. conducted an alternative study of linear self-assembling DNA hydrogels which further supports this need for flexibility in the internal structure to enhance macroscopic stiffness [65]. Specifically, 2-3 short DNA strands were designed to hybridize sequentially with one strand designed with a short 10 nt sticky overhang that could hybridize to another long tiled dsDNA strand with a self-complementary overhang. The length of the tiled dsDNA was designed to be rigid, with full complementary dsDNA regions between crosslinks, or flexible, with 30 nt thymidine repeats between crosslinks, with interchangeable parts (Figure 1d). These rigid and flexible designs were mixed in fractions between 100, 50, 25, and 0% of rigid linkers at approximately 4% \(w/v\) DNA content. The respective mixtures were found to have the corresponding storage moduli of 450, 600, 1800 and 1800 Pa at frequencies between 0.1-10 Hz and gelling temperatures of 40.1, 43.6, 49.4, and 48.7 \({}^{\circ}\)C [65]. This example as well demonstrated counterintuitive results where a greater fraction of flexible linkers increased the storage moduli, which was due to an increased number of hybridized crosslinks with the flexible linkers. However,  
Figure 1: Structural DNA hydrogel design. (**a**) Hydrogel formation by entanglement of RCA-produced concatemeric DNA strands. (**b**) Hydrogel formed by crosslinking of two RCA-produced ssDNA. (**c**) Hydrogels formed by hybridization of multivalent DNA nanostars. (**d**) Hydrogels formed by hybridization of linear sections of dsDNA. when flexible linkers were introduced to DNAns based gels they caused a decrease in the storage modulus [66]. [PERSON] et al. studied the formation a trivalent DNAns hydrogel with rigid sticky ends and sticky ends with 6 nt poly-T region between the sticky end and the dsDNA arm of the structure [66]. Their design allowed for enough flexibility in the linkers that they could self-hybridize with linkers from another arm on the same structure, thus also limiting the degree of connectivity between different structures. The flexible system only showed soft gel-like rheological properties near the melting temperature (T\({}_{\rm m}\)) of the linker (52 \({}^{\circ}\)C) with a storage modulus < 1 Pa greater than the loss modulus at frequencies below 10\({}^{3}\) Hz, whereas the nonflexible linkers showed a high-frequency plateau modulus of 45 Pa at 10\({}^{4}\) Hz at 44 \({}^{\circ}\)C and melted at 52 \({}^{\circ}\)C [66]. With regards to DNAns based hydrogel designs, valency presents an additional degree of freedom for mechanical design. [PERSON] et al. studied the role of DNAns valency (f) ranging from 3 to 6 with 20 base-pair (bp) arm lengths and a 7 nt sticky end separated by a nonbinding adenine base to allow for a slightly greater degree of flexibility.