  Liquid-liquid phase separation of intrinsically disordered proteins (IDPs) is
a major undergirding factor in the regulated formation of membraneless
organelles in the cell. The phase behavior of an IDP is sensitive to its amino
acid sequence. Here we apply a recent random-phase-approximation polymer theory
to investigate how the tendency for multiple chains of a protein to phase
separate, as characterized by the critical temperature $T^*_{\rm cr}$, is
related to the protein's single-chain average radius of gyration $\langle
R_{\rm g} \rangle$. For a set of sequences containing different permutations of
an equal number of positively and negatively charged residues, we found a
striking correlation $T^*_{\rm cr}\sim \langle R_{\rm g} \rangle^{-\gamma}$
with $\gamma$ as large as $\sim 6.0$, indicating that electrostatic effects
have similarly significant impact on promoting single-chain conformational
compactness and phase separation. Moreover, $T^*_{\rm cr}\propto -{\rm SCD}$,
where SCD is a recently proposed "sequence charge decoration" parameter
determined solely by sequence information. Ramifications of our findings for
deciphering the sequence dependence of IDP phase separation are discussed.
