  Intrinsically disordered proteins (IDPs) are typically low in
nonpolar/hydrophobic but relatively high in polar, charged, and aromatic amino
acid compositions. Some IDPs undergo liquid-liquid phase separation in the
aqueous milieu of the living cell. The resulting phase with enhanced IDP
concentration can function as a major component of membraneless organelles
that, by creating their own IDP-rich microenvironments, stimulate critical
biological functions. IDP phase behaviors are governed by their amino acid
sequences. To make progress in understanding this sequence-phase relationship,
we report further advances in a recently introduced application of
random-phase-approximation (RPA) heteropolymer theory to account for
sequence-specific electrostatics in IDP phase separation. Here we examine
computed variations in phase behavior with respect to block length and charge
density of model polyampholytes of alternating equal-length charge blocks to
gain insight into trends observed in IDP phase separation. As a real-life
example, the theory is applied to rationalize/predict binodal and spinodal
phase behaviors of the 236-residue N-terminal disordered region of RNA helicase
Ddx4 and its charge-scrambled mutant for which experimental data are available.
Fundamental differences are noted between the phase diagrams predicted by RPA
and those predicted by mean-field Flory-Huggins and
Overbeek-Voorn/Debye-H\"uckel theories. In the RPA context, a physically
plausible dependence of relative permittivity on protein concentration can
produce a cooperative effect in favor of IDP-IDP attraction and thus a
significant increased tendency to phase separate. Ramifications of these
findings for future development of IDP phase separation theory are discussed.
