Liquid-liquid phase separation of a polymer-rich phase from a polymer-dilute solution, known generally as coacervation, has been observed in a variety of biomolecular systems. Understanding of this process, and the properties of the resulting liquid, has been hampered in typical systems by the complexity of the components and of the intermolecular interactions. Here, we examine a single-component system comprised entirely of DNA, in which tetravalent DNA nanostar particles condense into liquids through attractive bonds formed from basepairing interactions. We measure the density, viscosity, particle self-diffusion, and surface tension of NS-liquid droplets. The sequence- and salt-dependent thermodynamics of basepairing accounts for most properties, particularly indicating that particle transport is an activated process whose barrier is the breaking of a single bond, and that very few bonds are broken at the surface. However, more complex effects are also seen. The relation of density to salt shows that electrostatic screening compacts the NS particles. Further, the interrelation of the transport properties indicates a breakdown of the Stokes-Einstein relation. This observation, in concert with the low surface tension and single-bond transport barrier, suggests this DNA liquid has a heterogeneous, clustered structure that is likely enabled by internal NS particle flexibility. We discuss these results in comparison to other coacervate systems.

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/

Liquid-liquid phase separation (LLPS) in macromolecular solutions (e.g. coacervation) is relevant both to technology, and to the process of mesoscale structure formation in cells. The LLPS process is characterized by a phase diagram, i.e. binodal lines in the temperature/concentration plane, which must be quantified to predict the system's behavior.Experimentally, this can be difficult due to complications in handling the dense macromolecular phase.Here, we develop a method for accurately quantifying the phase diagram without direct handling:We confine the sample within micron-scale, water-in-oil emulsion droplets, then use precision fluorescent imaging to measure the volume fraction of the condensate within the droplet.We find this volume fraction grows linearly with macromolecule concentration; thus, by applying the lever rule, we can directly extract the dense and dilute binodal concentrations.We use this approach to study a model LLPS system of self-assembled, fixed-valence DNA particles termed nanostars (NSs).We find that temperature/concentration phase diagrams of NSs display, with certain exceptions, a larger co-existence regime upon increasing salt or valence, in line with expectations.Aspects of the measured phase behavior validate recent predictions that account for the role of valence in modulating the connectivity of the condensed phase.Generally, our results on NS phase diagrams give fundamental insight into limited-valence phase separation, while the method we have developed will likely be useful in the study of other LLPS systems.