Increasing valence pushes DNA nanostar networks to the isostatic point

Abstract

The classic picture of soft material mechanics is that of rubber elasticity, in which material modulus is related to the entropic elasticity of flexible polymeric linkers. The rubber model, however, largely ignores the role of valence (i.e., the number of network chains emanating from a junction). Recent work predicts that valence, and particularly the Maxwell isostatic point, plays a key role in determining the mechanics of semiflexible polymer networks. Here, we report a series of experiments confirming the prominent role of valence in determining the mechanics of a model system. The system is based on DNA nanostars (DNAns): multiarmed, self-assembled nanostructures that form thermoreversible equilibrium gels through base paircontrolled cross-linking. We measure the linear and nonlinear elastic properties of these gels as a function of DNAns arm number, f, and concentration [DNAns]. We find that, as f increases from three to six, the gel's high-frequency plateau modulus strongly increases, and its dependence on [DNAns] transitions from nonlinear to linear. Additionally, higher-valence gels exhibit less strain hardening, indicating that they have less configurational freedom. Minimal strain hardening and linear dependence of shear modulus on concentration at high f are consistent with predictions for isostatic systems. Evident strain hardening and nonlinear concentration dependence of shear modulus suggest that the low-f networks are subisostatic and have a transient, potentially fractal percolated structure. Overall, our observations indicate that network elasticity is sensitive both to entropic elasticity of network chains and to junction valence, with an apparent isostatic point 5 < fc ≤ 6 in agreement with the Maxwell prediction.DNA nanostars | equilibrium gels | network mechanics | network valence | isostatic network This article contains supporting information online at www.pnas.org/lookup/suppl/

Mechanical Properties of DNA Hydrogels: Towards Highly Programmable Biomaterials

“…This study of valency was inspired by Maxwell's rigidity criterion, which predicts that a 3D network must have six beams emanating from each junction in order to be rigid. With~500 uM of DNAns for 3, 4, 5, and 6 arms, corresponding to~2.3, 3.0, 3.8, and 4.6% w/v, a plateau storage modulus of approximately 215, 1240, 2140, and 5810 Pa was observed at a frequency of 100 Hz [63]. Moreover, when valency was compared at equivalent volume fractions of DNA an increased storage moduli correlated with the increase in valency.…”

“…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].…”

Enzymatic degradation of liquid droplets of DNA is modulated near the phase boundary

“…A DNA nanostar consists of multiple double-stranded DNA arms emanating from a common three-or four-way junction, with each arm terminating in a single-stranded region (a sticky end). Hybridization of sticky ends causes nanostars to bind each other, driving phase separation (24) and the formation of viscoelastic liquids, whose behavior can be controlled through sequence design (25)(26)(27)(28). DNA nanostars condense into a liquid, rather than a crystalline solid or kinetically arrested gel, due to the reduced particle valence (24,29), the labile sticky ends, and the internal particle flexibility induced by the presence of unpaired bases at the junction and near the sticky end (30,31).…”

Scalable One-Pot-Liquid-Phase Oligonucleotide Synthesis for Model Network Hydrogels

“…This relaxation time scale corresponds to significantly enhanced stability than for comparable multi-arm DNA hydrogel systems, which generally show relaxation times in the range of 0.1 to 10 seconds. 26,[72][73][74] This may be the the result of the PEG-DNA network nature, which provides more flexibility compared to the stiff all-DNA networks. From a material perspective, it is important to emphasize that these gels have storage moduli G' > 1000 Pa and form self-standing, shape-persistent gels with sizes of several cm 3 ( Figure 5b), while most other DNA gels known to date have very limited shape stability under their own weight and feature G' values in the range of a few Pa to 100 Pa.…”