Direct and indirect salt effects on homotypic phase separation

Biomolecular condensates formed via liquid–liquid phase separation (LLPS) mediate a variety of cellular functions such as biogenesis of the ribosome and stress response (Mitrea et al., 2018; Protter and Parker, 2016). The driver for phase separation or condensation is intermolecular interactions, including electrostatic, hydrogen bonding, π–π, cation–π, amino–π, and hydrophobic (Das et al., 2020; Dignon et al., 2020; Zhou et al., 2024). Salt can tune all these interactions and thus exert significant effects on phase separation. While the screening effect of salt on electrostatic interactions is well-known, its effects on other types of interactions may be indirect and perhaps are less appreciated. In particular, high salt strengthens hydrophobic interactions by increasing the surface tension of water (Baldwin, 1996; Zhou and Pang, 2018). Because salt can exert disparate effects on different types of interactions, it can be used as a perturbation to dissect the relative importance of these interactions in phase separation (Farag et al., 2023; Hazra and Levy, 2023). Inside cells, proteins can encounter varying salt conditions at different locations or at different times, and therefore the drive for their phase separation can span a wide range.

Numerous studies of salt effects on protein phase separation have been reported. The most typical effect is the suppression of phase separation by screening electrostatic attraction, both for homotypic systems (Berry et al., 2015; Zhang et al., 2015; Brady et al., 2017; Strom et al., 2017; Wei et al., 2017; Reed and Hammer, 2018; Tsang et al., 2019; Martin et al., 2021; Lin et al., 2024) and for heterotypic systems (Farag et al., 2023; Galvanetto et al., 2023). However, salt can also promote phase separation, although the mechanism is not always clear (Martin et al., 2021; Muschol and Rosenberger, 1997; Burke et al., 2015; Kim et al., 2017; Dao et al., 2018; Babinchak et al., 2019; Le Ferrand et al., 2019; Wong et al., 2020; Agarwal et al., 2021; Krainer et al., 2021; Otis and Sharpe, 2022). In particular, Krainer et al., 2021 observed a ‘reentrant’ salt effect on the phase separation of five intrinsically disordered proteins (IDPs): phase separation occurs without salt, is prohibited by medium salt, and reemerges at high salt. They attributed the reemergence of phase separation to strengthened π-type and hydrophobic interactions that overcompensate weakened electrostatic attraction. A unifying understanding of how salt affects the phase separation of IDPs is still lacking. For example, it is an open question whether salt effects on phase separation can be predicted from the protein sequence. Deep knowledge, in particular at the atomic level, of how salt affects intermolecular interactions and, ultimately, phase separation is required.

The low-complexity domain of hnRNPA1 (A1-LCD) represents another IDP where an atypical salt effect was reported (Martin et al., 2021). The full-length protein, comprising folded domains along with the LCD, phase separates in the absence of salt and the tendency to phase separate is reduced upon adding salt, thus exhibiting the typical salt effect. A screening mechanism, specifically of electrostatic attraction between the LCD and the folded domains, is supported by small-angle X-ray scattering and coarse-grained molecular dynamics (MD) simulations. In contrast, A1-LCD does not phase separate without salt and starts to do so only after 100 mM NaCl is added. An earlier study revealed that π-types of interactions, mediated by aromatic residues, drive the phase separation of A1-LCD (Martin et al., 2020). A follow-up study, based on charge mutations, further showed that the net charge plays a strong suppressive role (Bremer et al., 2022). The saturation concentration (C_sat) for phase separation is minimum at a net charge near 0, and increases by two orders of magnitude, signifying an enormous weakening of the drive for phase separation, when the net charge moves away from neutrality in either direction. In a more recent study, salt promoted the homotypic phase separation of both A1-LCD and FUS-LCD, but suppressed the heterotypic phase separation of their mixture (Farag et al., 2023). The salt effect on the phase separation of A1-LCD was modeled by a Debye–Hückel potential in coarse-grained simulations (Tesei and Lindorff-Larsen, 2022). Similarly, the salt effect on the phase separation of another IDP, Ddx4, was analyzed using the random phase approximation based on a coarse-grained representation (Lin et al., 2024; Lin et al., 2016; Lin et al., 2020). Coarse-grained simulations with explicit water and ions have been used to study salt effects in both homotypic and heterotypic phase separation (Garaizar and Espinosa, 2021).

All-atom MD simulations can uniquely provide mechanistic insight into the driving force and properties of biomolecular condensates (Zhou et al., 2024). For example, these simulations showed that ATP, a small molecule with a −4 charge, bridges between positively charged IDP chains in driving phase separation (Kota et al., 2024). The intermolecular interactions quickly break and reform, explaining why the condensates can rapidly fuse despite very high macroscopic viscosity. Similarly, quick breakup and reformation of salt bridges in a heterotypic condensate allow the protein molecules to be extremely dynamic in a highly viscous environment (Galvanetto et al., 2023). Recently, all-atom MD simulations provided explanations for wide variations in phase equilibrium and material properties among condensates of tetrapeptides with different amino-acid compositions (Zhang et al., 2024). These and other simulations (Rekhi et al., 2024) show that all attractive residue–residue contacts contribute to the drive for phase separation.

Here, we study salt effects on A1-LCD condensation by all-atom MD simulations. The simulations reveal two direct effects and one indirect effect of NaCl: neutralization of net charge and bridging between protein chains and strengthening of π-type interactions by drawing water away from the interaction partners. We also present a unified picture of salt dependences of phase separation by defining four distinct classes and predict these classes from amino-acid composition.

We have shown in atomistic detail the actions of ions in the condensation of A1-LCD over a wide range of NaCl concentrations. The MD simulations reveal that NaCl has both direct and indirect effects in driving phase separation. The first direct effect is to neutralize the net charge of A1-LCD and thereby attenuate net charge repulsion. The second direct effect is to bridge between protein chains and thereby fortify intermolecular interaction networks. In addition, high salt strengthens π-types of interactions by drawing water away from the interaction partners, thereby also indirectly driving phase separation. The net result is that, while phase separation of A1-LCD is prevented by net charge repulsion at low salt, it is enabled at intermediate salt through charge neutralization and chain bridging by ions. The drive for phase separation becomes even stronger at high salt, where π-types of interactions are strengthened.

These findings broaden our understanding of the roles of charges and ions in phase separation. That high net charge is a suppressive factor is highlighted by the strong effect of A1-LCD charge mutations on C_sat (Bremer et al., 2022). Here, we have shown that this suppressive action can be countered by the addition of salt, which exerts both direct and indirect effects. One of these direct effects, that is, neutralization of net charge, can be treated by a Debye–Hückel potential in coarse-grained simulations (Tesei and Lindorff-Larsen, 2022). However, our all-atom explicit-solvent simulations have revealed not only an additional direct effect, that is, bridging between protein chains, but also an indirect effect, that is, strengthening of π-type interactions. In lattice Monte Carlo simulations of a system of charged homopolymer chains plus counterions with Coulomb interactions between all charges, counterions were found to occupy sites between chains and produce effective chain–chain attraction (Orkoulas et al., 2003); this effect might be viewed as a primitive form of bridging. Krainer et al., 2021 observed a reentrant salt effect on the phase separation of IDPs, and attributed the reemergence of phase separation at high salt to strengthened π-type and hydrophobic interactions that overcompensate weakened electrostatic attraction. Their conclusion was based on the salt dependences of the potentials of mean force calculated for pairs of sidechains of various types. Instead of a single pair of sidechains, our simulations are on multiple copies of protein chains. We show that, at high salt, the number of salt bridges remains constant while the numbers of π-types of interactions are elevated in the multi-chain system. Our simulations further reveal that high salt achieves the latter effect by drawing water away from π-interaction partners.

The present work puts us in a position to paint a unified picture of salt dependences of homotypic phase separation (Figure 6A, B and Table 1). The salt dependence that is most often reported is screening, where salts weaken the electrostatic attraction between protein chains and thereby suppress phase separation (Berry et al., 2015; Zhang et al., 2015; Brady et al., 2017; Strom et al., 2017; Wei et al., 2017; Reed and Hammer, 2018; Tsang et al., 2019; Martin et al., 2021; Lin et al., 2024). The reentrant salt dependence reported by Krainer et al., 2021 can be seen as an extension of the screening scenario, whereby high salt overcompensates the screening effect by strengthening π-type and hydrophobic interactions and leads to reemergence of phase separation. The high net charge scenario represented by A1-LCD is similar to the reentrant scenario at high salt but differs from it at low salt, where phase separation is prevented by net charge repulsion (Martin et al., 2021; Muschol and Rosenberger, 1997; Kim et al., 2017; Dao et al., 2018; Babinchak et al., 2019; Le Ferrand et al., 2019; Wong et al., 2020; Agarwal et al., 2021; Otis and Sharpe, 2022). In this class of salt dependence, a certain amount of salt is required to start phase separation. For A1-LCD, this minimum salt is ~100 mM NaCl (Martin et al., 2021). The recombinant mussel foot protein-1 (RMFP-1) presents an extreme example, which has a net charge of +24 over a sequence length of 121 and requires up to 700 mM NaCl to begin phase separation (Kim et al., 2017). The fourth class of salt dependence is a variation of the preceding one; here, the net charge is low and no significant net charge repulsion is expected, so the protein can phase separate even without salt. For example, FUS-LCD has a low net charge of −2 and phase separates without salt (Burke et al., 2015). The difference between the high and low net charge scenarios is well captured by the phase-separation behaviors of TDP43-LCD at two pHs (Babinchak et al., 2019). At pH 7, this protein has a relatively low net charge of +5 and phase separates without salt; the salt dependence thus belongs to the low net charge class. When pH is lowered to 4, the six His residues in the purification tag become positively charged, raising the net charge to +11; now phase separation requires 300 mM NaCl and the salt dependence switches to the high net charge class.

Figure 6

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We can not only rationalize the four distinct classes of salt dependence but also start to predict them from the amino-acid composition of the protein (Figure 6C and Table 1). The foregoing physical understanding suggests three determinants of salt dependence class: (1) the total number of charged residues, which determines the contribution of electrostatic interactions to the drive for phase separation and the importance of salt screening; (2) the net charge, which determines the magnitude of net charge repulsion; and (3) the total number of aromatic residues, which determines whether phase separation reemerges at high salt. We predict that the screening class occurs when the charged content is high but the net charge and aromatic content are low (Figure 6C). The other three classes of salt dependence all require a high aromatic content. For the reentrant class, the increase in aromatic content is the only difference from the screening class. For the high net charge class, the net charge obviously has to be high, but that could also mean at least a moderately high charged content. Finally, the low net charge class is predicted when the net charge is low but no bias is required of the charged content. The amino-acid compositional data in Table 1 validate these predictions. For example, of the 17 proteins in the classes of salt dependence that call for a high aromatic content, 12 (or 71%) actually have this feature (aromatic content >an 8% threshold). In contrast, of the 10 proteins in the class of salt dependence (i.e., ‘screening’) that calls for a low aromatic content, only 2 (or 20%) have an aromatic content above the threshold. In the latter two cases it remains to be tested whether phase separation would reemerge at much higher salt (and thereby resulting in a reclassification to reentrant). Likewise, of the 10 proteins in the class of salt dependence (i.e., ‘high net charge’) that calls for a high net charge, 7 (or 70%) actually have this feature (net charge >a 6% threshold). In contrast, of the 17 proteins in the classes of salt dependence that call for a low net charge, none has a net charge above the threshold. Lastly, of the 15 proteins in the classes of salt dependence that call for a high charge content, 11 (or 73%) actually have this feature (charged content >a 20% threshold). In comparison, of the 12 proteins in the classes of salt dependence that do not require a high charge content, only 2 (or 17%) have a charge content above the threshold.

Two of the proteins included in Table 1 are Caprin1 and its phosphorylated variant pY-Caprin1. Caprin1’s phase separation required 500 mM NaCl and was promoted by higher salt (Wong et al., 2020), and thus behaved as if in the high net charge class of salt dependence (Figure 6A, third panel). In contrast, pY-Caprin1’s phase separation was suppressed by salt (Lin et al., 2024), behaving as if in the screening class (Figure 6A, first panel). Our amino-acid composition-based predictor correctly places both proteins in these respective classes (Table 1), with Caprin1’s sequence possessing both a high net charge and a high aromatic content whereas pY-Caprin1’s sequence possessing a high level of charged residues. The disparate salt dependences of these two proteins were also correctly captured by both analytical theory and coarse-grained simulations (Lin et al., 2024). The simulations also showed the dominance of Cl^– over Na⁺ in partitioning into the dense phase of Caprin1, similar to our all-atom simulations of A1-LCD (Figure 3B); both Caprin1 and A1-LCD have a high net positive charge.

Comparing and contrasting coarse-grained simulations and all-atom simulations highlight the pros and cons of the two approaches. Coarse-grained simulations can readily capture the phase-separation process and represent the equilibrium between the dense and dilute phases. For short peptides, all-atom simulations have been shown to accomplish both of these tasks (Zhang et al., 2024). For the mixture of ATP and a 33-residue IDP, all-atom simulations were able to capture the condensation process but not the equilibration of the resulting dense phase with a dilute phase (Kota et al., 2024). In this work, although the total number of atoms in the A1-LCD system, ~half a million, is very high from a computational standpoint, the number of protein chains (i.e., 8) is still too low for a proper representation of a homogenous solution at low salt and a full equilibration between two phases at intermediate and high salt. Nevertheless, our simulations do not show condensation at low salt, thus mimicking a homogenous solution; the simulations at intermediate and high salt show condensation and thus model the dense phase. We are thus able to compare the salt effects in a homogenous solution (50 mM NaCl) and in the dense phase after phase separation (150–1000 mM NaCl) and compare the salt effects in dense phases with intermediate (150 and 300 mM NaCl) and high condensation (500 and 1000 mM NaCl). Importantly, the all-atom simulations are able to capture unusual physical effects that could be missed in coarse-grained simulations, such as strengthening π-types of interactions by drawing water away from the interaction partners. The latter effect is now confirmed by Raman spectroscopy (Joshi et al., 2024).

To conclude, salts regulate intermolecular interactions in biomolecular condensates in a variety of ways, but the net dependence of homotypic phase separation on salt concentration can be placed into four distinct classes (Figure 6A, B). Moreover, these classes are predictable from the protein amino-acid composition. Salts also exert significant effects on heterotypic condensates (Farag et al., 2023; Galvanetto et al., 2023); the conclusions drawn here on homotypic condensates may prove instructive for heterotypic condensates. The fact that different IDPs respond to salts differently raises interesting questions on phase separation inside cells. For example, a fluctuation in intracellular salt concentration may promote the phase separation of some IDPs and suppress the phase separation of other IDPs. If two IDPs co-phase separate or form heterotypic condensates, salt fluctuations may change the protein composition of condensates and the relative contributions of the individual proteins to phase separation. Lastly, we note that the atomistic details of ion coordination to A1-LCD backbone or sidechain groups are reminiscent of those observed in other systems, in particular channels and transporters for Na⁺ and Cl^– (Mancusso et al., 2012; Mita et al., 2021; Leisle et al., 2022).

All data generated or analyzed during this study are included in the manuscript and supplementary files, including source data for figures.

1. 1. Agarwal A
   2. Rai SK
   3. Avni A
   4. Mukhopadhyay S

   (2021) An intrinsically disordered pathological prion variant Y145Stop converts into self-seeding amyloids via liquid-liquid phase separation

   PNAS 118:118.

   https://doi.org/10.1073/pnas.2100968118

   • PubMed
   • Google Scholar
2. 1. Babinchak WM
   2. Haider R
   3. Dumm BK
   4. Sarkar P
   5. Surewicz K
   6. Choi JK
   7. Surewicz WK

   (2019) The role of liquid-liquid phase separation in aggregation of the TDP-43 low-complexity domain

   The Journal of Biological Chemistry 294:6306–6317.

   https://doi.org/10.1074/jbc.RA118.007222

   • PubMed
   • Google Scholar
3. 1. Baldwin RL

   (1996) How Hofmeister ion interactions affect protein stability

   Biophysical Journal 71:2056–2063.

   https://doi.org/10.1016/S0006-3495(96)79404-3

   • PubMed
   • Google Scholar
4. 1. Berendsen HJC
   2. Postma JPM
   3. van Gunsteren WF
   4. DiNola A
   5. Haak JR

   (1984) Molecular dynamics with coupling to an external bath

   The Journal of Chemical Physics 81:3684–3690.

   https://doi.org/10.1063/1.448118

   • Google Scholar
5. 1. Berry J
   2. Weber SC
   3. Vaidya N
   4. Haataja M
   5. Brangwynne CP

   (2015) RNA transcription modulates phase transition-driven nuclear body assembly

   PNAS 112:E5237–E5245.

   https://doi.org/10.1073/pnas.1509317112

   • PubMed
   • Google Scholar
6. 1. Brady JP
   2. Farber PJ
   3. Sekhar A
   4. Lin Y-H
   5. Huang R
   6. Bah A
   7. Nott TJ
   8. Chan HS
   9. Baldwin AJ
   10. Forman-Kay JD
   11. Kay LE

   (2017) Structural and hydrodynamic properties of an intrinsically disordered region of a germ cell-specific protein on phase separation

   PNAS 114:E8194–E8203.

   https://doi.org/10.1073/pnas.1706197114

   • PubMed
   • Google Scholar
7. 1. Bremer A
   2. Farag M
   3. Borcherds WM
   4. Peran I
   5. Martin EW
   6. Pappu RV
   7. Mittag T

   (2022) Deciphering how naturally occurring sequence features impact the phase behaviours of disordered prion-like domains

   Nature Chemistry 14:196–207.

   https://doi.org/10.1038/s41557-021-00840-w

   • PubMed
   • Google Scholar
8. 1. Burke KA
   2. Janke AM
   3. Rhine CL
   4. Fawzi NL

   (2015) Residue-by-residue view of in vitro FUS granules that bind the C-terminal domain of RNA polymerase II

   Molecular Cell 60:231–241.

   https://doi.org/10.1016/j.molcel.2015.09.006

   • PubMed
   • Google Scholar
9. Book

   1. Case DA
   2. Ben-Shalom IY
   3. Brozell SR
   4. Cerutti DS
   5. Cheatham TE
   6. Cruzeiro VWD
   7. Darden TA
   8. Duke RE
   9. Ghoreishi D
   10. Gilson MK

   (2018)

   AMBER

   San Francisco: University of California.

   • Google Scholar
10. 1. Dao TP
    2. Kolaitis RM
    3. Kim HJ
    4. O’Donovan K
    5. Martyniak B
    6. Colicino E
    7. Hehnly H
    8. Taylor JP
    9. Castañeda CA

    (2018) Ubiquitin modulates liquid-liquid phase separation of UBQLN2 via disruption of multivalent interactions

    Molecular Cell 69:965–978.

    https://doi.org/10.1016/j.molcel.2018.02.004

    • PubMed
    • Google Scholar
11. 1. Das S
    2. Lin YH
    3. Vernon RM
    4. Forman-Kay JD
    5. Chan HS

    (2020) Comparative roles of charge, π, and hydrophobic interactions in sequence-dependent phase separation of intrinsically disordered proteins

    PNAS 117:28795–28805.

    https://doi.org/10.1073/pnas.2008122117

    • PubMed
    • Google Scholar
12. 1. Dey S
    2. MacAinsh M
    3. Zhou HX

    (2022) Sequence-dependent backbone dynamics of intrinsically disordered proteins

    Journal of Chemical Theory and Computation 18:6310–6323.

    https://doi.org/10.1021/acs.jctc.2c00328

    • PubMed
    • Google Scholar
13. 1. Dignon GL
    2. Best RB
    3. Mittal J

    (2020) Biomolecular phase separation: from molecular driving forces to macroscopic properties

    Annual Review of Physical Chemistry 71:53–75.

    https://doi.org/10.1146/annurev-physchem-071819-113553

    • PubMed
    • Google Scholar
14. 1. Essmann U
    2. Perera L
    3. Berkowitz ML
    4. Darden T
    5. Lee H
    6. Pedersen LG

    (1995) A smooth particle mesh Ewald method

    The Journal of Chemical Physics 103:8577–8593.

    https://doi.org/10.1063/1.470117

    • Google Scholar
15. 1. Farag M
    2. Borcherds WM
    3. Bremer A
    4. Mittag T
    5. Pappu RV

    (2023) Phase separation of protein mixtures is driven by the interplay of homotypic and heterotypic interactions

    Nature Communications 14:5527.

    https://doi.org/10.1038/s41467-023-41274-x

    • PubMed
    • Google Scholar
16. 1. Galvanetto N
    2. Ivanović MT
    3. Chowdhury A
    4. Sottini A
    5. Nüesch MF
    6. Nettels D
    7. Best RB
    8. Schuler B

    (2023) Extreme dynamics in a biomolecular condensate

    Nature 619:876–883.

    https://doi.org/10.1038/s41586-023-06329-5

    • PubMed
    • Google Scholar
17. 1. Garaizar A
    2. Espinosa JR

    (2021) Salt dependent phase behavior of intrinsically disordered proteins from a coarse-grained model with explicit water and ions

    The Journal of Chemical Physics 155:155.

    https://doi.org/10.1063/5.0062687

    • PubMed
    • Google Scholar
18. 1. Hazra MK
    2. Levy Y

    (2023) Cross-talk of cation-π interactions with electrostatic and aromatic interactions: a salt-dependent trade-off in biomolecular condensates

    The Journal of Physical Chemistry Letters 14:8460–8469.

    https://doi.org/10.1021/acs.jpclett.3c01642

    • PubMed
    • Google Scholar
19. 1. Humphrey W
    2. Dalke A
    3. Schulten K

    (1996) VMD: visual molecular dynamics

    Journal of Molecular Graphics 14:33–38.

    https://doi.org/10.1016/0263-7855(96)00018-5

    • PubMed
    • Google Scholar
20. 1. Joshi A
    2. Avni A
    3. Walimbe A
    4. Rai SK
    5. Sarkar S
    6. Mukhopadhyay S

    (2024) Hydrogen-bonded network of water in phase-separated biomolecular condensates

    The Journal of Physical Chemistry Letters 15:7724–7734.

    https://doi.org/10.1021/acs.jpclett.4c01153

    • PubMed
    • Google Scholar
21. 1. Kim S
    2. Yoo HY
    3. Huang J
    4. Lee Y
    5. Park S
    6. Park Y
    7. Jin S
    8. Jung YM
    9. Zeng H
    10. Hwang DS
    11. Jho Y

    (2017) Salt triggers the simple coacervation of an underwater adhesive when cations meet aromatic π electrons in seawater

    ACS Nano 11:6764–6772.

    https://doi.org/10.1021/acsnano.7b01370

    • Google Scholar
22. 1. Kota D
    2. Prasad R
    3. Zhou HX

    (2024) Adenosine triphosphate mediates phase separation of disordered basic proteins by bridging intermolecular interaction networks

    Journal of the American Chemical Society 146:1326–1336.

    https://doi.org/10.1021/jacs.3c09134

    • PubMed
    • Google Scholar
23. 1. Krainer G
    2. Welsh TJ
    3. Joseph JA
    4. Espinosa JR
    5. Wittmann S
    6. de Csilléry E
    7. Sridhar A
    8. Toprakcioglu Z
    9. Gudiškytė G
    10. Czekalska MA
    11. Arter WE
    12. Guillén-Boixet J
    13. Franzmann TM
    14. Qamar S
    15. George-Hyslop PS
    16. Hyman AA
    17. Collepardo-Guevara R
    18. Alberti S
    19. Knowles TPJ

    (2021) Reentrant liquid condensate phase of proteins is stabilized by hydrophobic and non-ionic interactions

    Nature Communications 12:1085.

    https://doi.org/10.1038/s41467-021-21181-9

    • PubMed
    • Google Scholar
24. 1. Le Ferrand H
    2. Duchamp M
    3. Gabryelczyk B
    4. Cai H
    5. Miserez A

    (2019) Time-resolved observations of liquid-liquid phase separation at the nanoscale using in situ liquid transmission electron microscopy

    Journal of the American Chemical Society 141:7202–7210.

    https://doi.org/10.1021/jacs.9b03083

    • PubMed
    • Google Scholar
25. 1. Leisle L
    2. Lam K
    3. Dehghani-Ghahnaviyeh S
    4. Fortea E
    5. Galpin JD
    6. Ahern CA
    7. Tajkhorshid E
    8. Accardi A

    (2022) Backbone amides are determinants of Cl− selectivity in CLC ion channels

    Nature Communications 13:7508.

    https://doi.org/10.1038/s41467-022-35279-1

    • Google Scholar
26. 1. Lin YH
    2. Forman-Kay JD
    3. Chan HS

    (2016) Sequence-specific polyampholyte phase separation in membraneless organelles

    Physical Review Letters 117:178101.

    https://doi.org/10.1103/PhysRevLett.117.178101

    • PubMed
    • Google Scholar
27. 1. Lin YH
    2. Brady JP
    3. Chan HS
    4. Ghosh K

    (2020) A unified analytical theory of heteropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes

    The Journal of Chemical Physics 152:045102.

    https://doi.org/10.1063/1.5139661

    • PubMed
    • Google Scholar
28. 1. Lin YH
    2. Kim TH
    3. Das S
    4. Pal T
    5. Wessén J
    6. Rangadurai AK
    7. Kay LE
    8. Forman-Kay JD
    9. Chan HS

    (2024) Electrostatics of Salt-dependent reentrant phase behaviors highlights diverse roles of ATP in biomolecular condensates

    eLife 10:100284.1.

    https://doi.org/10.7554/eLife.100284.1

    • Google Scholar
29. 1. Maier JA
    2. Martinez C
    3. Kasavajhala K
    4. Wickstrom L
    5. Hauser KE
    6. Simmerling C ff

    (2015) ff14SB: improving the accuracy of protein side chain and backbone parameters from ff99SB

    Journal of Chemical Theory and Computation 11:3696–3713.

    https://doi.org/10.1021/acs.jctc.5b00255

    • PubMed
    • Google Scholar
30. 1. Mancusso R
    2. Gregorio GG
    3. Liu Q
    4. Wang DN

    (2012) Structure and mechanism of a bacterial sodium-dependent dicarboxylate transporter

    Nature 491:622–626.

    https://doi.org/10.1038/nature11542

    • PubMed
    • Google Scholar
31. 1. Martin EW
    2. Holehouse AS
    3. Peran I
    4. Farag M
    5. Incicco JJ
    6. Bremer A
    7. Grace CR
    8. Soranno A
    9. Pappu RV
    10. Mittag T

    (2020) Valence and patterning of aromatic residues determine the phase behavior of prion-like domains

    Science 367:694–699.

    https://doi.org/10.1126/science.aaw8653

    • PubMed
    • Google Scholar
32. 1. Martin EW
    2. Thomasen FE
    3. Milkovic NM
    4. Cuneo MJ
    5. Grace CR
    6. Nourse A
    7. Lindorff-Larsen K
    8. Mittag T

    (2021) Interplay of folded domains and the disordered low-complexity domain in mediating hnRNPA1 phase separation

    Nucleic Acids Research 49:2931–2945.

    https://doi.org/10.1093/nar/gkab063

    • PubMed
    • Google Scholar
33. 1. Mita K
    2. Sumikama T
    3. Iwamoto M
    4. Matsuki Y
    5. Shigemi K
    6. Oiki S

    (2021) Conductance selectivity of Na(+) across the K(+) channel via Na(+) trapped in a tortuous trajectory

    PNAS 118:e2017168118.

    https://doi.org/10.1073/pnas.2017168118

    • Google Scholar
34. 1. Mitrea DM
    2. Cika JA
    3. Stanley CB
    4. Nourse A
    5. Onuchic PL
    6. Banerjee PR
    7. Phillips AH
    8. Park CG
    9. Deniz AA
    10. Kriwacki RW

    (2018) Self-interaction of NPM1 modulates multiple mechanisms of liquid-liquid phase separation

    Nature Communications 9:842.

    https://doi.org/10.1038/s41467-018-03255-3

    • PubMed
    • Google Scholar
35. 1. Muschol M
    2. Rosenberger F

    (1997) Liquid–liquid phase separation in supersaturated lysozyme solutions and associated precipitate formation/crystallization

    The Journal of Chemical Physics 107:1953–1962.

    https://doi.org/10.1063/1.474547

    • Google Scholar
36. 1. Orkoulas G
    2. Kumar SK
    3. Panagiotopoulos AZ

    (2003) Monte carlo study of coulombic criticality in polyelectrolytes

    Physical Review Letters 90:048303.

    https://doi.org/10.1103/PhysRevLett.90.048303

    • PubMed
    • Google Scholar
37. 1. Otis JB
    2. Sharpe S

    (2022) Sequence context and complex hofmeister salt interactions dictate phase separation propensity of resilin-like polypeptides

    Biomacromolecules 23:5225–5238.

    https://doi.org/10.1021/acs.biomac.2c01027

    • PubMed
    • Google Scholar
38. 1. Pastor RW
    2. Brooks BR
    3. Szabo A

    (1988) An analysis of the accuracy of Langevin and molecular dynamics algorithms

    Molecular Physics 65:1409–1419.

    https://doi.org/10.1080/00268978800101881

    • Google Scholar
39. 1. Piana S
    2. Donchev AG
    3. Robustelli P
    4. Shaw DE

    (2015) Water dispersion interactions strongly influence simulated structural properties of disordered protein states

    The Journal of Physical Chemistry. B 119:5113–5123.

    https://doi.org/10.1021/jp508971m

    • PubMed
    • Google Scholar
40. 1. Protter DSW
    2. Parker R

    (2016) Principles and properties of stress granules

    Trends in Cell Biology 26:668–679.

    https://doi.org/10.1016/j.tcb.2016.05.004

    • PubMed
    • Google Scholar
41. 1. Reed EH
    2. Hammer DA

    (2018) Redox sensitive protein droplets from recombinant oleosin

    Soft Matter 14:6506–6513.

    https://doi.org/10.1039/c8sm01047a

    • PubMed
    • Google Scholar
42. 1. Rekhi S
    2. Garcia CG
    3. Barai M
    4. Rizuan A
    5. Schuster BS
    6. Kiick KL
    7. Mittal J

    (2024) Expanding the molecular language of protein liquid-liquid phase separation

    Nature Chemistry 16:1113–1124.

    https://doi.org/10.1038/s41557-024-01489-x

    • PubMed
    • Google Scholar
43. 1. Roe DR
    2. Cheatham TE

    (2013) PTRAJ and CPPTRAJ: software for processing and analysis of molecular dynamics trajectory data

    Journal of Chemical Theory and Computation 9:3084–3095.

    https://doi.org/10.1021/ct400341p

    • PubMed
    • Google Scholar
44. 1. Ryckaert JP
    2. Ciccotti G
    3. Berendsen HJC

    (1977) Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes

    Journal of Computational Physics 23:327–341.

    https://doi.org/10.1016/0021-9991(77)90098-5

    • Google Scholar
45. 1. Salomon-Ferrer R
    2. Götz AW
    3. Poole D
    4. Le Grand S
    5. Walker RC

    (2013) Routine microsecond molecular dynamics simulations with AMBER on GPUs. 2. explicit solvent particle mesh ewald

    Journal of Chemical Theory and Computation 9:3878–3888.

    https://doi.org/10.1021/ct400314y

    • PubMed
    • Google Scholar
46. 1. Strom AR
    2. Emelyanov AV
    3. Mir M
    4. Fyodorov DV
    5. Darzacq X
    6. Karpen GH

    (2017) Phase separation drives heterochromatin domain formation

    Nature 547:241–245.

    https://doi.org/10.1038/nature22989

    • PubMed
    • Google Scholar
47. 1. Tesei G
    2. Lindorff-Larsen K

    (2022) Improved predictions of phase behaviour of intrinsically disordered proteins by tuning the interaction range

    Open Research Europe 2:94.

    https://doi.org/10.12688/openreseurope.14967.2

    • PubMed
    • Google Scholar
48. 1. Tsang B
    2. Arsenault J
    3. Vernon RM
    4. Lin H
    5. Sonenberg N
    6. Wang LY
    7. Bah A
    8. Forman-Kay JD

    (2019) Phosphoregulated FMRP phase separation models activity-dependent translation through bidirectional control of mRNA granule formation

    PNAS 116:4218–4227.

    https://doi.org/10.1073/pnas.1814385116

    • PubMed
    • Google Scholar
49. 1. Wei M-T
    2. Elbaum-Garfinkle S
    3. Holehouse AS
    4. Chen CC-H
    5. Feric M
    6. Arnold CB
    7. Priestley RD
    8. Pappu RV
    9. Brangwynne CP

    (2017) Phase behaviour of disordered proteins underlying low density and high permeability of liquid organelles

    Nature Chemistry 9:1118–1125.

    https://doi.org/10.1038/nchem.2803

    • PubMed
    • Google Scholar
50. 1. Wong LE
    2. Kim TH
    3. Muhandiram DR
    4. Forman-Kay JD
    5. Kay LE

    (2020) NMR experiments for studies of dilute and condensed protein phases: application to the phase-separating protein CAPRIN1

    Journal of the American Chemical Society 142:2471–2489.

    https://doi.org/10.1021/jacs.9b12208

    • PubMed
    • Google Scholar
51. 1. Zhang H
    2. Elbaum-Garfinkle S
    3. Langdon EM
    4. Taylor N
    5. Occhipinti P
    6. Bridges AA
    7. Brangwynne CP
    8. Gladfelter AS

    (2015) RNA Controls PolyQ protein phase transitions

    Molecular Cell 60:220–230.

    https://doi.org/10.1016/j.molcel.2015.09.017

    • PubMed
    • Google Scholar
52. 1. Zhang Y
    2. Prasad R
    3. Su S
    4. Lee D
    5. Zhou HX

    (2024) Amino acid-dependent phase equilibrium and material properties of tetrapeptide condensates

    Cell Reports Physical Science 5:102218.

    https://doi.org/10.1016/j.xcrp.2024.102218

    • Google Scholar
53. 1. Zhou HX
    2. Pang X

    (2018) Electrostatic interactions in protein structure, folding, binding, and condensation

    Chemical Reviews 118:1691–1741.

    https://doi.org/10.1021/acs.chemrev.7b00305

    • PubMed
    • Google Scholar
54. Software

    1. Zhou HX

    (2024) Salt_on_A1LCD_LLPS, version swh:1:rev:50aba4df0876042ec81fecc91dc8cc05fea44108

    Software Heritage.

    https://archive.softwareheritage.org/swh:1:dir:fb72711af603e599e1b56c41100a4187a3826342;origin=https://github.com/hzhou43/Salt_on_A1LCD_LLPS;visit=swh:1:snp:4d71154beb71a7f8e6cfec5fbca7eb3fa08a97b7;anchor=swh:1:rev:50aba4df0876042ec81fecc91dc8cc05fea44108
55. 1. Zhou HX
    2. Kota D
    3. Qin S
    4. Prasad R

    (2024) Fundamental aspects of phase-separated biomolecular condensates

    Chemical Reviews 124:8550–8595.

    https://doi.org/10.1021/acs.chemrev.4c00138

    • PubMed
    • Google Scholar

Author details

1. Matt MacAinsh

   Department of Chemistry, University of Illinois Chicago, Chicago, United States

   Contribution

   Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft

   Competing interests

   No competing interests declared

2. Souvik Dey

   Department of Chemistry, University of Illinois Chicago, Chicago, United States

   Contribution

   Conceptualization, Data curation, Investigation

   Competing interests

   No competing interests declared

3. Huan-Xiang Zhou

   1. Department of Chemistry, University of Illinois Chicago, Chicago, United States
   2. Department of Physics, University of Illinois Chicago, Chicago, United States

   Contribution

   Conceptualization, Formal analysis, Supervision, Funding acquisition, Validation, Visualization, Writing - original draft, Project administration, Writing - review and editing

   For correspondence

   hzhou43@uic.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9020-0302