Accurate phase diagram of tetravalent DNA nanostars

We evaluate, by means of molecular dynamics simulations employing a realistic DNA coarse-grained model, the phase behaviour and the structural and dynamic properties of tetravalent DNA nanostars, i.e. nanoconstructs completely made of DNA. We find that, as the system is cooled down, tetramers undergo a gas--liquid phase separation in a region of concentrations which, if the difference in salt concentration is taken into account, is comparable with the recently measured experimental phase diagram [S. Biffi \textit{et al}, Proc. Natl. Acad. Sci, \textbf{110}, 15633 (2013)]. We also present a mean-field free energy for modelling the phase diagram based on the bonding contribution, derived by Wertheim in its studies of associating liquids, combined with mass action law expressions appropriate for DNA binding and a numerically evaluated reference free energy. The resulting free energy qualitatively reproduces the numerical data. Finally, we report information on the nanostar structure, e.g. geometry and flexibility of the single tetramer and of the collective behaviour, providing a useful reference for future small angle scattering experiments, for all investigated temperatures and concentrations.