  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.
