Phase separation and single-chain compactness of charged disordered proteins are strongly correlated

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.