  Motivated by the idea that intrinsically disordered proteins (IDPs) condense
into liquid-like droplets within cells, we carry out Monte Carlo simulations of
a polymer lattice model to study the relationship between charge patterning and
phase separation. Polymer chains containing neutral, positively charged and
negatively charged monomers are placed on a cubic lattice. Only nearest
neighbor interactions between charges are considered. We determine the phase
diagram for a systematically varied set of sequences. We observe homogeneous
fluids, liquid condensation, cluster phases, filaments, and crystal states. Of
the six sequences we study, three form crystals at low temperatures. The other
three sequences, which have lower charge densities, instead collapse into
gel-like networks or unconnected finite clusters. Longer neutral patches along
the sequence sterically limit the size and shape of low-energy structures,
which is analogous to the effect of charge or limited valence in attractive
colloids. Only one sequence clearly exhibits liquid behavior; this sequence has
a reduced tendency to individually fold and crystallize compared to others of
similar charge density and draws parallels to real IDP behavior.
