Biomolecular condensates undergirded by phase separations of proteins and nucleic acids serve crucial biological functions. To gain physical insights into their genetic basis, we study how liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) depends on their sequence charge patterns using a coarse-grained model wherein each amino acid residue is represented by a bead on a chain configured in real space. Phase diagrams are determined by Langevin dynamics. Charge patterns are characterized by the `blockiness' measure \kappa and the `sequence charge decoration' (SCD) parameter. Consistent with random phase approximation (RPA) theory and lattice simulations, LLPS propensity ( critical temperature T^*_{\rm cr} ) increases with increasingly negative SCD for a set of sequences showing a positive correlation between \kappa and -SCD. Relative to RPA predictions, however, the simulated sequence-dependent variation in T^*_{\rm cr} is often---though not always---smaller, whereas the simulated critical volume fractions are higher. In contrast , for a set of sequences exhibiting an anti-correlation between \kappa and -SCD, the simulated T^*_{\rm cr}'s are---contrary to RPA prediction---quite insensitive to \kappa or SCD . Additionally, we find that  the LLPS propensity of IDPs with a strictly alternating charge sequence might have been overestimated because stabilizing interactions among such sequences require spatial alignments that are more difficult to achieve in real space than stipulated by RPA or lattice models. Taken together, our results underscore both the utility and limitations of RPA as well as the \kappa and SCD parameters . Further efforts will be needed to rationalize the newly observed subtleties.
Biomolecular condensates undergirded by phase separations of proteins and nucleic acids serve crucial biological functions. To gain physical insights into their genetic basis, we study how liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) depends on their sequence charge patterns using a continuum Langevin chain model wherein each amino acid residue is represented by a single bead. Charge patterns are characterized by the `blockiness' measure \kappa and the `sequence charge decoration' (SCD) parameter. Consistent with random phase approximation (RPA) theory and lattice simulations, LLPS propensity as characterized by critical temperature T^*_{\rm cr} increases with increasingly negative SCD for a set of sequences showing a positive correlation between \kappa and -SCD. Relative to RPA , the simulated sequence-dependent variation in T^*_{\rm cr} is often---though not always---smaller, whereas the simulated critical volume fractions are higher. However , for a set of sequences exhibiting an anti-correlation between \kappa and -SCD, the simulated T^*_{\rm cr}'s are quite insensitive to either parameters . Additionally, we find that blocky sequences that allow for strong electrostatic repulsion can lead to coexistence curves with upward concavity as stipulated by RPA, but the LLPS propensity of a strictly alternating charge sequence was likely overestimated by RPA and lattice models because interchain stabilization of this sequence requires spatial alignments that are difficult to achieve in real space . These results help delineate the utility and limitations of the charge pattern parameters and of RPA, pointing to further efforts necessary for rationalizing the newly observed subtleties.
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