# Mechanical Properties of DNA Hydrogels: Towards Highly Programmable Biomaterials
## 5 Dissecting the Mechanical Properties of DNA Hydrogels
### Dynamic Properties of DNA Hydrogels  
DNA hydrogels, particularly DNAns hydrogels, present a unique system with a high-degree of control which can be utilized to mimic other complex materials for further study. Specifically, [PERSON] et al. observed a two-step decay in the correlation function during probe-free DLS measurements, which resembles a property seen in glassy materials [118]. This two-step decay correlates with a fast and slow time constant representing the vibrations of the system and network reorganization, respectively (Figure 4c). A later study utilizing multiangle DLS, [PERSON] et al. found the slow relaxation time to be length-scale independent above the minimum wavevector used, 8 \(\upmu\)m\({}^{-1}\), which corresponds to a length-scale \(\sim\)780 nm comprising tens of DNAns at \(\sim\)14 nm in length [119]. This length-independent relaxation time suggests that the relaxation time is also weakly dependent on concentration but follows an Arrhenius equation with regards to temperature dependence [119]. A later study by [PERSON] et al. explored the lower wavevector regime down to 0.2 \(\upmu\)m\({}^{-1}\), and as large as 30 \(\upmu\)m\({}^{-1}\) corresponding to length-scales of 31 and 0.2 \(\upmu\)m, respectively. They found that at larger length-scales the slow-relaxation time becomes dependent on the length-scale by an exponent of two, attributed to diffusive processes [107]. Interestingly, the point of transition between dependence and independence of length scale is temperature-dependent, with lower temperatures resulting in a larger length-scale for transition in agreement with a larger degree of association at lower temperatures. Furthermore, [PERSON] et al. replicated the length-scale independent region with a simulation composed of a linear chain of beads and springs for which there were two different spring constants. Each spring dynamically changes between stiffnesses in order to replicate the local changes in bulk modulus due to localized network reorganization in DNAns gels [107]. The formation of clusters during DNAns gel formation was studied by [PERSON] et al. using DLS and variable ratios of tetravalent DNAs to linker. They found that at low temperatures a percolating network was formed regardless of the ratio, however, the ratio affected the formation of clusters at higher temperatures and thus could be used as a factor to program the formation of the gel [120]. As previously mentioned, [PERSON] et al. studied the effect of DNAns valency on DNA hydrogels at different concentrations ranging from 200-800 \(\upmu\)M of DNAns. At \(\sim\)500 \(\upmu\)M of DNAns the plateau modulus increased from 100 to 4000 Pa with valency from 3 to 6, and although a higher valency implies a higher DNA content per structure, they show that a valency of 6 still results in a plateau modulus an order of magnitude greater than for the equivalent volume fraction of trivalent DNAs [63]. Additionally, while there was a small change in the crossover frequency at different valencies, the temperature dependence was identical for each valency and followed an Arrhenius equation; further validating the notion that the hybridization energy of the interunit linkage is responsible for the timescale of network reorganization [63]. [PERSON] et al. used their previously mentioned coarse-grained model to extract the contributions of the DNA arm rigidity, angular constraint, and interunit hybridization to the storage modulus at different frequencies [117]. They found that the arm rigidity was responsible for over 90% of the storage modulus and largely independent of frequency, while the angular constraints contributed to only a few percent of the total storage modulus and was similarly frequency independent. Interestingly, the contribution due to interunit hybridization was two orders of magnitude less than the total plateau modulus at low frequencies, however, it increased by almost an order of magnitude at higher frequencies.