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

Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS) of proteins, we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess roles of electrostatic, hydrophobic, cation-π, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated three different residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation-π interactions consistently accounted for available experimental LLPS data on the wild-type, a charge-scrambled, a phenylalanine-to-alanine (FtoA), and an arginine-to-lysine (RtoK) mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, important LLPS-driving π-related interactions are embodied in classical statistical potentials. Further elucidation is necessary, however, especially of phenylalanine's role in condensate assembly because experiments on FtoA and tyrosine-to-phenylalanine mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than posited by common statistical potentials. Protein-protein electrostatic interactions are modulated by relative permittivity, which in general depends on aqueous protein concentration. Analytical theory suggests that this dependence entails enhanced interprotein interactions in the condensed phase but more favorable protein-solvent interactions in the dilute phase. The opposing trends lead to only a modest overall impact on LLPS.

Assembly of model postsynaptic densities involves interactions auxiliary to stoichiometric binding.

The assembly of functional biomolecular condensates often involves liquid-liquid phase separation (LLPS) of proteins with multiple modular domains, which can be folded or conformationally disordered to various degrees. To understand the LLPS-driving domain-domain interactions, a fundamental question is how readily the interactions in the condensed phase can be inferred from interdomain interactions in dilute solutions. In particular, are the interactions leading to LLPS exclusively those underlying the formation of discrete interdomain complexes in homogeneous solutions? We address this question by developing a mean-field LLPS theory of two stoichiometrically constrained solute species. The theory is applied to the neuronal proteins SynGAP and PSD-95, whose complex coacervate serves as a rudimentary model for neuronal postsynaptic densities (PSDs). The predicted phase behaviors are compared with experiments. Previously, a three SynGAP/two PSD-95 ratio was determined for SynGAP/PSD-95 complexes in dilute solutions. However, when this 3:2 stoichiometry is uniformly imposed in our theory encompassing both dilute and condensed phases, the tie-line pattern of the predicted SynGAP/PSD-95 phase diagram differs drastically from that obtained experimentally. In contrast, theories embodying alternate scenarios postulating auxiliary SynGAP-PSD-95 as well as SynGAP-SynGAP and PSD-95-PSD-95 interactions, in addition to those responsible for stoichiometric SynGAP/PSD-95 complexes, produce tie-line patterns consistent with experiment. Hence, our combined theoretical-experimental analysis indicates that weaker interactions or higher-order complexes beyond the 3:2 stoichiometry, but not yet documented, are involved in the formation of SynGAP/PSD-95 condensates, imploring future efforts to ascertain the nature of these auxiliary interactions in PSD-like LLPS and underscoring a likely general synergy between stoichiometric, structurally specific binding and stochastic, multivalent "fuzzy" interactions in the assembly of functional biomolecular condensates.

Field theory description of ion association in re-entrant phase separation of polyampholytes.

Phase separation of several different overall neutral polyampholyte species (with zero net charge) is studied in solution with two oppositely charged ion species that can form ion pairs through an association reaction. Hereby, a field theory description of the system, which treats polyampholyte charge sequence dependent electrostatic interactions as well as excluded volume effects, is given. Interestingly, analysis of the model using random phase approximation and field theoretic simulation consistently shows evidence of a re-entrant polyampholyte phase separation at high ion concentrations when there is an overall decrease of volume upon ion association. As an illustration of the ramifications of our theoretical framework, several polyampholyte concentration vs ion concentration phase diagrams under constant temperature conditions are presented to elucidate the dependence of phase separation behavior on the polyampholyte sequence charge pattern as well as ion pair dissociation constant, volumetric effects on ion association, solvent quality, and temperature.

Pressure Sensitivity of SynGAP/PSD-95 Condensates as a Model for Postsynaptic Densities and Its Biophysical and Neurological Ramifications.

Biomolecular condensates consisting of proteins and nucleic acids can serve critical biological functions, so that some condensates are referred as membraneless organelles. They can also be disease-causing, if their assembly is misregulated. A major physicochemical basis of the formation of biomolecular condensates is liquid-liquid phase separation (LLPS). In general, LLPS depends on environmental variables, such as temperature and hydrostatic pressure. The effects of pressure on the LLPS of a binary SynGAP/PSD-95 protein system mimicking postsynaptic densities, which are protein assemblies underneath the plasma membrane of excitatory synapses, were investigated. Quite unexpectedly, the model system LLPS is much more sensitive to pressure than the folded states of typical globular proteins. Phase-separated droplets of SynGAP/PSD-95 were found to dissolve into a homogeneous solution already at ten-to-hundred bar levels. The pressure sensitivity of SynGAP/PSD-95 is seen here as a consequence of both pressure-dependent multivalent interaction strength and void volume effects. Considering that organisms in the deep sea are under pressures up to about 1 kbar, this implies that deep-sea organisms have to devise means to counteract this high pressure sensitivity of biomolecular condensates to avoid harm. Intriguingly, these findings may shed light on the biophysical underpinning of pressure-related neurological disorders in terrestrial vertebrates.

A unified analytical theory of heteropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes.

The physical chemistry of liquid-liquid phase separation (LLPS) of polymer solutions bears directly on the assembly of biologically functional dropletlike bodies from proteins and nucleic acids. These biomolecular condensates include certain extracellular materials and intracellular compartments that are characterized as "membraneless organelles." Analytical theories are a valuable, computationally efficient tool for addressing general principles. LLPS of neutral homopolymers is quite well described by theory, but it has been a challenge to develop general theories for the LLPS of heteropolymers involving charge-charge interactions. Here, we present a theory that combines a random-phase-approximation treatment of polymer density fluctuations and an account of intrachain conformational heterogeneity based on renormalized Kuhn lengths to provide predictions of LLPS properties as a function of pH, salt, and charge patterning along the chain sequence. Advancing beyond more limited analytical approaches, our LLPS theory is applicable to a wide variety of charged sequences ranging from highly charged polyelectrolytes to neutral or nearly neutral polyampholytes. This theory should be useful in high-throughput screening of protein and other sequences for their LLPS propensities and can serve as a basis for more comprehensive theories that incorporate nonelectrostatic interactions. Experimental ramifications of our theory are discussed.

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

Membrane encapsulation is frequently used by the cell to sequester biomolecules and compartmentalize their function. Cells also concentrate molecules into phase-separated protein or protein/nucleic acid "membraneless organelles" that regulate a host of biochemical processes. Here, we use solution NMR spectroscopy to study phase-separated droplets formed from the intrinsically disordered N-terminal 236 residues of the germ-granule protein Ddx4. We show that the protein within the concentrated phase of phase-separated Ddx4, [Formula: see text], diffuses as a particle of 600-nm hydrodynamic radius dissolved in water. However, NMR spectra reveal sharp resonances with chemical shifts showing [Formula: see text] to be intrinsically disordered. Spin relaxation measurements indicate that the backbone amides of [Formula: see text] have significant mobility, explaining why high-resolution spectra are observed, but motion is reduced compared with an equivalently concentrated nonphase-separating control. Observation of a network of interchain interactions, as established by NOE spectroscopy, shows the importance of Phe and Arg interactions in driving the phase separation of Ddx4, while the salt dependence of both low- and high-concentration regions of phase diagrams establishes an important role for electrostatic interactions. The diffusion of a series of small probes and the compact but disordered 4E binding protein 2 (4E-BP2) protein in [Formula: see text] are explained by an excluded volume effect, similar to that found for globular protein solvents. No changes in structural propensities of 4E-BP2 dissolved in [Formula: see text] are observed, while changes to DNA and RNA molecules have been reported, highlighting the diverse roles that proteinaceous solvents play in dictating the properties of dissolved solutes.

Pressure-Sensitive and Osmolyte-Modulated Liquid-Liquid Phase Separation of Eye-Lens γ-Crystallins.

Biomolecular condensates can be functional (e.g., as membrane-less organelles) or dysfunctional (e.g., as precursors to pathological protein aggregates). A major physical underpinning of biomolecular condensates is liquid-liquid phase separation (LLPS) of proteins and nucleic acids. Here we investigate the effects of temperature and pressure on the LLPS of the eye-lens protein γ-crystallin using UV/vis and IR absorption, fluorescence spectroscopy, and light microscopy to characterize the mesoscopic phase states. Quite unexpectedly, the LLPS of γ-crystallin is much more sensitive to pressure than folded states of globular proteins. At low temperatures, the phase-separated droplets of γ-crystallin dissolve into a homogeneous solution at as low as ∼0.1 kbar whereas proteins typically unfold above ∼3 kbar. This observation suggests, in general, that organisms thriving under high-pressure conditions in the deep sea, with pressure of up to 1 kbar, have to cope with this pressure sensitivity of biomolecular condensates to avoid detrimental impacts to their physiology. Interestingly, our experiments demonstrate that trimethylamine- N-oxide, an osmolyte upregulated in deep-sea fish, significantly enhances the stability of the condensed protein droplets, pointing to a previously unrecognized aspect of the adaptive advantage of increased concentrations of osmolytes in deep-sea organisms. As the birth place of life on earth could have been the deep sea, studies of pressure effects on LLPS as presented here are relevant to the possible formation of protocells under prebiotic conditions. A physical framework to conceptualize our observations and further ramifications of biomolecular LLPS at low temperatures and high hydrostatic pressures is discussed.

Temperature, Hydrostatic Pressure, and Osmolyte Effects on Liquid-Liquid Phase Separation in Protein Condensates: Physical Chemistry and Biological Implications.

Liquid-liquid phase separation (LLPS) of proteins and other biomolecules play a critical role in the organization of extracellular materials and membrane-less compartmentalization of intra-organismal spaces through the formation of condensates. Structural properties of such mesoscopic droplet-like states were studied by spectroscopy, microscopy, and other biophysical techniques. The temperature dependence of biomolecular LLPS has been studied extensively, indicating that phase-separated condensed states of proteins can be stabilized or destabilized by increasing temperature. In contrast, the physical and biological significance of hydrostatic pressure on LLPS is less appreciated. Summarized here are recent investigations of protein LLPS under pressures up to the kbar-regime. Strikingly, for the cases studied thus far, LLPSs of both globular proteins and intrinsically disordered proteins/regions are typically more sensitive to pressure than the folding of proteins, suggesting that organisms inhabiting the deep sea and sub-seafloor sediments, under pressures up to 1 kbar and beyond, have to mitigate this pressure-sensitivity to avoid unwanted destabilization of their functional biomolecular condensates. Interestingly, we found that trimethylamine-N-oxide (TMAO), an osmolyte upregulated in deep-sea fish, can significantly stabilize protein droplets under pressure, pointing to another adaptive advantage for increased TMAO concentrations in deep-sea organisms besides the osmolyte's stabilizing effect against protein unfolding. As life on Earth might have originated in the deep sea, pressure-dependent LLPS is pertinent to questions regarding prebiotic proto-cells. Herein, we offer a conceptual framework for rationalizing the recent experimental findings and present an outline of the basic thermodynamics of temperature-, pressure-, and osmolyte-dependent LLPS as well as a molecular-level statistical mechanics picture in terms of solvent-mediated interactions and void volumes.

Theories for Sequence-Dependent Phase Behaviors of Biomolecular Condensates.

Liquid-liquid phase separation and related condensation processes of intrinsically disordered proteins (IDPs), proteins with intrinsically disordered regions, and nucleic acids underpin various condensed-liquid droplets or gel-like assemblies in the cellular environment. Collectively referred to as condensates, these bodies provide spatial/temporal compartmentalization, often serving as hubs for regulated biomolecular interactions. Examples include certain extracellular materials, transcription complexes, and membraneless organelles such as germ and stress granules and the nucleolus. They are critically important to cellular function; thus misregulation of their assembly is implicated in many diseases. Biomolecular condensates are complex entities. Our understanding of their inner workings is only in its infancy. Nonetheless, insights into basic biophysical principles of their assembly can be gained by applying analytical theories to elucidate how IDP phase behaviors are governed by the properties of the multivalent, solvent-mediated interactions entailed by the proteins' amino acid sequences. Here we briefly review the background of the pertinent polymer theories and outline the approximations that enable a tractable theoretical account of the dependence of IDP phase behaviors on the charge pattern of the IDP sequence. Of relevance to the homeostatic assembly of compositionally and functionally distinct condensates in the cellular context, theory indicates that the propensity for populations of different IDP sequences to mix or demix upon phase separation is affected by the similarity or dissimilarity of the sequence charge patterns. We also explore prospects of extending analytical theories to account for dynamic aspects of biomolecular condensates and to incorporate effects of cation-π, π-π, and temperature-dependent hydrophobic interactions on IDP phase properties.

Pressure-Induced Dissolution and Reentrant Formation of Condensed, Liquid-Liquid Phase-Separated Elastomeric α-Elastin.

We investigated the combined effects of temperature and pressure on liquid-liquid phase separation (LLPS) phenomena of α-elastin up to the multi-kbar regime. FT-IR spectroscopy, CD, UV/Vis absorption, phase-contrast light and fluorescence microscopy techniques were employed to reveal structural changes and mesoscopic phase states of the system. A novel pressure-induced reentrant LLPS was observed in the intermediate temperature range. A molecular-level picture, in particular on the role of hydrophobic interactions, hydration, and void volume in controlling LLPS phenomena is presented. The potential role of the LLPS phenomena in the development of early cellular compartmentalization is discussed, which might have started in the deep sea, where pressures up to the kbar level are encountered.

Molecular recognition and packing frustration in a helical protein.

Biomolecular recognition entails attractive forces for the functional native states and discrimination against potential nonnative interactions that favor alternate stable configurations. The challenge posed by the competition of nonnative stabilization against native-centric forces is conceptualized as frustration. Experiment indicates that frustration is often minimal in evolved biological systems although nonnative possibilities are intuitively abundant. Much of the physical basis of minimal frustration in protein folding thus remains to be elucidated. Here we make progress by studying the colicin immunity protein Im9. To assess the energetic favorability of nonnative versus native interactions, we compute free energies of association of various combinations of the four helices in Im9 (referred to as H1, H2, H3, and H4) by extensive explicit-water molecular dynamics simulations (total simulated time > 300 µs), focusing primarily on the pairs with the largest native contact surfaces, H1-H2 and H1-H4. Frustration is detected in H1-H2 packing in that a nonnative packing orientation is significantly stabilized relative to native, whereas such a prominent nonnative effect is not observed for H1-H4 packing. However, in contrast to the favored nonnative H1-H2 packing in isolation, the native H1-H2 packing orientation is stabilized by H3 and loop residues surrounding H4. Taken together, these results showcase the contextual nature of molecular recognition, and suggest further that nonnative effects in H1-H2 packing may be largely avoided by the experimentally inferred Im9 folding transition state with native packing most developed at the H1-H4 rather than the H1-H2 interface.

Coarse-grained residue-based models of disordered protein condensates: utility and limitations of simple charge pattern parameters.

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 κ and the "sequence charge decoration" (SCD) parameter. Consistent with random phase approximation (RPA) theory and lattice simulations, LLPS propensity as characterized by critical temperature Tcr* increases with increasingly negative SCD for a set of sequences showing a positive correlation between κ and -SCD. Relative to RPA, the simulated sequence-dependent variation in Tcr* 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 κ and -SCD, the simulated Tcr*'s are quite insensitive to either parameter. 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.

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∗cr, is related to the protein's single-chain average radius of gyration 〈Rg〉. For a set of sequences containing different permutations of an equal number of positively and negatively charged residues, we found a striking correlation T∗cr ∼ 〈Rg〉-γ with γ as large as ∼6.0, indicating that electrostatic effects have similarly significant impact on promoting single-chain conformational compactness and phase separation. Moreover, T∗cr ∝ -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.

Conformational Heterogeneity and FRET Data Interpretation for Dimensions of Unfolded Proteins.

A mathematico-physically valid formulation is required to infer properties of disordered protein conformations from single-molecule Förster resonance energy transfer (smFRET). Conformational dimensions inferred by conventional approaches that presume a homogeneous conformational ensemble can be unphysical. When all possible-heterogeneous as well as homogeneous-conformational distributions are taken into account without prejudgment, a single value of average transfer efficiency 〈E〉 between dyes at two chain ends is generally consistent with highly diverse, multiple values of the average radius of gyration 〈Rg〉. Here we utilize unbiased conformational statistics from a coarse-grained explicit-chain model to establish a general logical framework to quantify this fundamental ambiguity in smFRET inference. As an application, we address the long-standing controversy regarding the denaturant dependence of 〈Rg〉 of unfolded proteins, focusing on Protein L as an example. Conventional smFRET inference concluded that 〈Rg〉 of unfolded Protein L is highly sensitive to [GuHCl], but data from SAXS suggested a near-constant 〈Rg〉 irrespective of [GuHCl]. Strikingly, our analysis indicates that although the reported 〈E〉 values for Protein L at [GuHCl] = 1 and 7 M are very different at 0.75 and 0.45, respectively, the Bayesian Rg2 distributions consistent with these two 〈E〉 values overlap by as much as 75%. Our findings suggest, in general, that the smFRET-SAXS discrepancy regarding unfolded protein dimensions likely arise from highly heterogeneous conformational ensembles at low or zero denaturant, and that additional experimental probes are needed to ascertain the nature of this heterogeneity.

Theoretical Insights into the Biophysics of Protein Bi-stability and Evolutionary Switches.

Deciphering the effects of nonsynonymous mutations on protein structure is central to many areas of biomedical research and is of fundamental importance to the study of molecular evolution. Much of the investigation of protein evolution has focused on mutations that leave a protein's folded structure essentially unchanged. However, to evolve novel folds of proteins, mutations that lead to large conformational modifications have to be involved. Unraveling the basic biophysics of such mutations is a challenge to theory, especially when only one or two amino acid substitutions cause a large-scale conformational switch. Among the few such mutational switches identified experimentally, the one between the GA all-α and GB α+ß folds is extensively characterized; but all-atom simulations using fully transferrable potentials have not been able to account for this striking switching behavior. Here we introduce an explicit-chain model that combines structure-based native biases for multiple alternative structures with a general physical atomic force field, and apply this construct to twelve mutants spanning the sequence variation between GA and GB. In agreement with experiment, we observe conformational switching from GA to GB upon a single L45Y substitution in the GA98 mutant. In line with the latent evolutionary potential concept, our model shows a gradual sequence-dependent change in fold preference in the mutants before this switch. Our analysis also indicates that a sharp GA/GB switch may arise from the orientation dependence of aromatic π-interactions. These findings provide physical insights toward rationalizing, predicting and designing evolutionary conformational switches.

A critical comparison of coarse-grained structure-based approaches and atomic models of protein folding.

Structure-based coarse-grained Go-like models have been used extensively in deciphering protein folding mechanisms because of their simplicity and tractability. Meanwhile, explicit-solvent molecular dynamics (MD) simulations with physics-based all-atom force fields have been applied successfully to simulate folding/unfolding transitions for several small, fast-folding proteins. To explore the degree to which coarse-grained Go-like models and their extensions to incorporate nonnative interactions are capable of producing folding processes similar to those in all-atom MD simulations, here we systematically compare the computed unfolded states, transition states, and transition paths obtained using coarse-grained models and all-atom explicit-solvent MD simulations. The conformations in the unfolded state in common Go models are more extended, and are thus more in line with experiment, than those from all-atom MD simulations. Nevertheless, the structural features of transition states obtained by the two types of models are largely similar. In contrast, the folding transition paths are significantly more sensitive to modeling details. In particular, when common Go-like models are augmented with nonnative interactions, the predicted dimensions of the unfolded conformations become similar to those computed using all-atom MD. With this connection, the large deviations of all-atom MD from simple diffusion theory are likely caused in part by the presence of significant nonnative effects in folding processes modelled by current atomic force fields. The ramifications of our findings to the application of coarse-grained modeling to more complex biomolecular systems are discussed.

Correction: A critical comparison of coarse-grained structure-based approaches and atomic models of protein folding.

Correction for 'A critical comparison of coarse-grained structure-based approaches and atomic models of protein folding' by Jie Hu et al., Phys. Chem. Chem. Phys., 2017, 19, 13629-13639.

Conformations of a Metastable SH3 Domain Characterized by smFRET and an Excluded-Volume Polymer Model.

Conformational states of the metastable drkN SH3 domain were characterized using single-molecule fluorescence techniques. Under nondenaturing conditions, two Förster resonance energy transfer (FRET) populations were observed that corresponded to a folded and an unfolded state. FRET-estimated radii of gyration and hydrodynamic radii estimated by fluorescence correlation spectroscopy of the two coexisting conformations are in agreement with previous ensemble x-ray scattering and NMR measurements. Surprisingly, when exposed to high concentrations of urea and GdmCl denaturants, the protein still exhibits two distinct FRET populations. The dominant conformation is expanded, showing a low FRET efficiency, consistent with the expected behavior of a random chain with excluded volume. However, approximately one-third of the drkN SH3 conformations showed high, nearly 100%, FRET efficiency, which is shown to correspond to denaturation-induced looped conformations that remain stable on a timescale of at least 100 µs. These loops may contain interconverting conformations that are more globally collapsed, hairpin-like, or circular, giving rise to the observed heterogeneous broadening of this population. Although the underlying mechanism of chain looping remains elusive, FRET experiments in formamide and dimethyl sulfoxide suggest that interactions between hydrophobic groups in the distal regions may play a significant role in the formation of the looped state.

Volumetric Physics of Polypeptide Coil-Helix Transitions.

Volumetric properties of proteins bear directly on their biological functions in hyperbaric environments and are useful in general as a biophysical probe. To gain insight into conformation-dependent protein volume, we developed an implicit-solvent atomic chain model that transparently embodies two physical origins of volume: (1) a fundamental geometric term capturing the van der Waals volume of the protein and the particulate, finite-size nature of the water molecules, modeled together by the volume encased by the protein's molecular surface, and (2) a physicochemical term for other solvation effects, accounted for by empirical proportionality relationships between experimental partial molar volumes and solvent-accessible surface areas of model compounds. We tested this construct by Langevin dynamics simulations of a 16-residue polyalanine. The simulated trajectories indicate an average volume decrease of 1.73 ± 0.1 Å3/residue for coil-helix transition, ∼80% of which is caused by a decrease in geometric void/cavity volume, and a robust positive activation volume for helical hydrogen bond formation originating from the transient void created by an approaching donor-acceptor pair and nearby atoms. These findings are consistent with prior experiments with alanine-rich peptides and offer an atomistic analysis of the observed overall volume changes. The results suggest, in general, that hydrostatic pressure likely stabilizes helical conformations of short peptides but slows the process of helix formation. In contrast, hydrostatic pressure is more likely to destabilize natural globular proteins because of the void volume entrapped in their folded structures. The conceptual framework of our model thus affords a coherent physical rationalization for experiments.

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.