Sequence-Specific Polyampholyte Phase Separation in Membraneless Organelles

Liquid-liquid phase separation of charge- and/or aromatic-enriched intrinsically disordered proteins (IDPs) is critical in the biological function of membraneless organelles. Much of the physics of this recent discovery remains to be elucidated. Here, we present a theory in the random phase approximation to account for electrostatic effects in polyampholyte phase separations, yielding predictions consistent with recent experiments on the IDP Ddx4. The theory is applicable to any charge pattern and thus provides a general analytical framework for studying sequence dependence of IDP phase separation.

Figure 1

Phase diagrams of $N=240$ salt-free polyampholytes with 4, 6, 8, and 12 alternating charge blocks of ${\sigma }_{\alpha }^{\text{block}}=(-1{)}^{\alpha -1}\sigma$; ${\varphi }_m$ and $T^{*}$ are, respectively, the dimensionless polymer volume ratio and the temperature (see the text). A dilute and a condensed phase exist, respectively, above and below each phase-boundary curve. (a) $\sigma =1$. (b) $\sigma =0.5$. The black dots are the critical points (${\varphi }_{\mathrm{cr}}$, $T_{\mathrm{cr}}^{*}$). Polyampholytes with fewer blocks and a stronger $\sigma$ phase separate at a higher $T^{*}$.

Figure 2

(a) The $\mathrm{Ddx}{4}^{\mathsf{N}1}$ (top panel) and $\mathrm{Ddx}{4}^{\mathsf{N}1}\mathrm{CS}$ (bottom panel) amino acid sequences. Positively ($+$) and negatively ($-$) charged (basic and acidic) and aromatic residues are highlighted, respectively, in red, turquoise, and yellow. (b) Charge patterns of the sequences ($+$, red; $-$, blue) indicate that the charges exhibit more blocklike properties (repeated red or repeated blue) and are less evenly dispersed in $\mathrm{Ddx}{4}^{\mathsf{N}1}$ than in $\mathrm{Ddx}{4}^{\mathsf{N}1}\mathrm{CS}$ (cf. Fig. 6A of Ref. [12]). (c) Theoretical phase diagrams computed by Eq. (3) under salt-free conditions. (d) $\mathrm{Ddx}{4}^{\mathsf{N}1}$ phase diagrams [Eq. (3)] for different monovalent salt (NaCl) concentrations.

Figure 3

(a) Theoretical phase diagrams of $\mathrm{Ddx}{4}^{\mathsf{N}1}$ under different [NaCl] values, computed by RPA theory augmented by FH short-range interactions (the curves), with fitted $\epsilon =29.5$, ${ϵ}_h=0.15$, and ${ϵ}_s=-0.3$ (see the text). Experimental data [12] are included for comparison (the symbols; same color code). (b) The salt-free phase diagrams of $\mathrm{Ddx}{4}^{\mathsf{N}1}$ and $\mathrm{Ddx}{4}^{\mathsf{N}1}\mathrm{CS}$ with and without the FH interaction in Eq. (10).