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Lin YH, Wessén J, Pal T, Das S, Chan HS. Numerical Techniques for Applications of Analytical Theories to Sequence-Dependent Phase Separations of Intrinsically Disordered Proteins. Methods Mol Biol 2023; 2563:51-94. [PMID: 36227468 DOI: 10.1007/978-1-0716-2663-4_3] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Biomolecular condensates, physically underpinned to a significant extent by liquid-liquid phase separation (LLPS), are now widely recognized by numerous experimental studies to be of fundamental biological, biomedical, and biophysical importance. In the face of experimental discoveries, analytical formulations emerged as a powerful yet tractable tool in recent theoretical investigations of the role of LLPS in the assembly and dissociation of these condensates. The pertinent LLPS often involves, though not exclusively, intrinsically disordered proteins engaging in multivalent interactions that are governed by their amino acid sequences. For researchers interested in applying these theoretical methods, here we provide a practical guide to a set of computational techniques devised for extracting sequence-dependent LLPS properties from analytical formulations. The numerical procedures covered include those for the determination of spinodal and binodal phase boundaries from a general free energy function with examples based on the random phase approximation in polymer theory, construction of tie lines for multiple-component LLPS, and field-theoretic simulation of multiple-chain heteropolymeric systems using complex Langevin dynamics. Since a more accurate physical picture often requires comparing analytical theory against explicit-chain model predictions, a commonly utilized methodology for coarse-grained molecular dynamics simulations of sequence-specific LLPS is also briefly outlined.
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Affiliation(s)
- Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, Toronto, ON, Canada
- Molecular Medicine, Hospital for Sick Children, Toronto, ON, Canada
| | - Jonas Wessén
- Department of Biochemistry, University of Toronto, Toronto, ON, Canada
| | - Tanmoy Pal
- Department of Biochemistry, University of Toronto, Toronto, ON, Canada
| | - Suman Das
- Department of Biochemistry, University of Toronto, Toronto, ON, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, ON, Canada.
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Wessén J, Das S, Pal T, Chan HS. Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Protein-Like Heteropolymers with Short- and Long-Spatial-Range Interactions. J Phys Chem B 2022; 126:9222-9245. [PMID: 36343363 DOI: 10.1021/acs.jpcb.2c06181] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
A theory for sequence-dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints. A mean-field approximation leads to an effective Flory-Huggins χ parameter, which, in conjunction with RPA, accounts for the contact-interaction effects of amino acid composition and the sequence-pattern effects of long-range electrostatics in IDP LLPS, whereas FTS based on the formulation provides full sequence dependence for both short- and long-range interactions. This general approach is illustrated here by applications to variants of a natural IDP in the context of several different amino-acid interaction schemes as well as a set of different model hydrophobic-polar sequences sharing the same composition. Effectiveness of the methodology is verified by coarse-grained explicit-chain molecular dynamics simulations.
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Affiliation(s)
- Jonas Wessén
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Suman Das
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Tanmoy Pal
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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Wessén J, Pal T, Chan HS. Field theory description of ion association in re-entrant phase separation of polyampholytes. J Chem Phys 2022; 156:194903. [DOI: 10.1063/5.0088326] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
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. A field theory description of the system, that treats polyampholyte charge sequence dependent electrostatic interactions as well as excluded volume effects, is hereby given. Interestingly, analysis of the model using random phase approximation and field theoretic simulation consistently show 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 polyampholyte sequence charge pattern as well as ion-pair dissociation constant, volumetric effects on ion association, solvent quality, and temperature.
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Affiliation(s)
- Jonas Wessén
- Department of Biochemsitry, University of Toronto, Canada
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Nilsson D, Bozorg B, Mohanty S, Söderberg B, Irbäck A. Limitations of field-theory simulation for exploring phase separation: The role of repulsion in a lattice protein model. J Chem Phys 2022; 156:015101. [PMID: 34998327 DOI: 10.1063/5.0070412] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Field-theory simulation by the complex Langevin method offers an alternative to conventional sampling techniques for exploring the forces driving biomolecular liquid-liquid phase separation. Such simulations have recently been used to study several polyampholyte systems. Here, we formulate a field theory corresponding to the hydrophobic/polar (HP) lattice protein model, with finite same-site repulsion and nearest-neighbor attraction between HH bead pairs. By direct comparison with particle-based Monte Carlo simulations, we show that complex Langevin sampling of the field theory reproduces the thermodynamic properties of the HP model only if the same-site repulsion is not too strong. Unfortunately, the repulsion has to be taken weaker than what is needed to prevent condensed droplets from assuming an artificially compact shape. Analysis of a minimal and analytically solvable toy model hints that the sampling problems caused by repulsive interaction may stem from loss of ergodicity.
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Affiliation(s)
- Daniel Nilsson
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
| | - Behruz Bozorg
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
| | - Sandipan Mohanty
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Bo Söderberg
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
| | - Anders Irbäck
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden
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Lin YH, Wu H, Jia B, Zhang M, Chan HS. Assembly of model postsynaptic densities involves interactions auxiliary to stoichiometric binding. Biophys J 2022; 121:157-171. [PMID: 34637756 PMCID: PMC8758407 DOI: 10.1016/j.bpj.2021.10.008] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2021] [Revised: 09/29/2021] [Accepted: 10/06/2021] [Indexed: 01/07/2023] Open
Abstract
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.
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Affiliation(s)
- Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, Toronto, Ontario, Canada,Molecular Medicine, The Hospital for Sick Children, Toronto, Ontario, Canada
| | - Haowei Wu
- Division of Life Science, State Key Laboratory of Molecular Neuroscience, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Bowen Jia
- Division of Life Science, State Key Laboratory of Molecular Neuroscience, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Mingjie Zhang
- Division of Life Science, State Key Laboratory of Molecular Neuroscience, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China,School of Life Sciences, Southern University of Science and Technology, Shenzhen, China,Corresponding author
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario, Canada,Corresponding author
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Joseph JA, Reinhardt A, Aguirre A, Chew PY, Russell KO, Espinosa JR, Garaizar A, Collepardo-Guevara R. Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy. NATURE COMPUTATIONAL SCIENCE 2021; 1:732-743. [PMID: 35795820 PMCID: PMC7612994 DOI: 10.1038/s43588-021-00155-3] [Citation(s) in RCA: 105] [Impact Index Per Article: 35.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Various physics- and data-driven sequence-dependent protein coarse-grained models have been developed to study biomolecular phase separation and elucidate the dominant physicochemical driving forces. Here, we present Mpipi, a multiscale coarse-grained model that describes almost quantitatively the change in protein critical temperatures as a function of amino-acid sequence. The model is parameterised from both atomistic simulations and bioinformatics data and accounts for the dominant role of π-π and hybrid cation-π/π-π interactions and the much stronger attractive contacts established by arginines than lysines. We provide a comprehensive set of benchmarks for Mpipi and seven other residue-level coarse-grained models against experimental radii of gyration and quantitative in-vitro phase diagrams; Mpipi predictions agree well with experiment on both fronts. Moreover, it can account for protein-RNA interactions, correctly predicts the multiphase behaviour of a charge-matched poly-arginine/poly-lysine/RNA system, and recapitulates experimental LLPS trends for sequence mutations on FUS, DDX4 and LAF-1 proteins.
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Affiliation(s)
- Jerelle A. Joseph
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
- Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
- Department of Genetics, University of Cambridge, Cambridge, CB2 3EH, UK
| | - Aleks Reinhardt
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
| | - Anne Aguirre
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
| | - Pin Yu Chew
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
| | - Kieran O. Russell
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
| | - Jorge R. Espinosa
- Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Adiran Garaizar
- Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Rosana Collepardo-Guevara
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK
- Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
- Department of Genetics, University of Cambridge, Cambridge, CB2 3EH, UK
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Nilsson D, Irbäck A. Finite-size shifts in simulated protein droplet phase diagrams. J Chem Phys 2021; 154:235101. [PMID: 34241264 DOI: 10.1063/5.0052813] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
Computer simulation can provide valuable insight into the forces driving biomolecular liquid-liquid phase separation. However, the simulated systems have a limited size, which makes it important to minimize and control finite-size effects. Here, using a phenomenological free-energy ansatz, we investigate how the single-phase densities observed in a canonical system under coexistence conditions depend on the system size and the total density. We compare the theoretical expectations with results from Monte Carlo simulations based on a simple hydrophobic/polar protein model. We consider both cubic systems with spherical droplets and elongated systems with slab-like droplets. The results presented suggest that the slab simulation method greatly facilitates the estimation of the coexistence densities in the large-system limit.
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Affiliation(s)
- Daniel Nilsson
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-223 62 Lund, Sweden
| | - Anders Irbäck
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-223 62 Lund, Sweden
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Pal T, Wessén J, Das S, Chan HS. Subcompartmentalization of polyampholyte species in organelle-like condensates is promoted by charge-pattern mismatch and strong excluded-volume interaction. Phys Rev E 2021; 103:042406. [PMID: 34005864 DOI: 10.1103/physreve.103.042406] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 03/11/2021] [Indexed: 06/12/2023]
Abstract
Polyampholyte field theory and explicit-chain molecular dynamics models of sequence-specific phase separation of a system with two intrinsically disordered protein (IDP) species indicate consistently that a substantial polymer excluded volume and a significant mismatch of the IDP sequence charge patterns can act in concert, but not in isolation, to demix the two IDP species upon condensation. This finding reveals an energetic-geometric interplay in a stochastic, "fuzzy" molecular recognition mechanism that may facilitate subcompartmentalization of membraneless organelles.
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Affiliation(s)
- Tanmoy Pal
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Jonas Wessén
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Suman Das
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, Ontario M5S 1A8, Canada
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Goetz SK, Mahamid J. Visualizing Molecular Architectures of Cellular Condensates: Hints of Complex Coacervation Scenarios. Dev Cell 2021; 55:97-107. [PMID: 33049214 DOI: 10.1016/j.devcel.2020.09.003] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Revised: 08/15/2020] [Accepted: 09/05/2020] [Indexed: 02/09/2023]
Abstract
In the last decade, liquid-liquid phase separation has emerged as a fundamental principle in the organization of crowded cellular environments into functionally distinct membraneless compartments. It is now established that biomolecules can condense into various physical phases, traditionally defined for simple polymer systems, and more recently elucidated by techniques employed in life sciences. We review pioneering cryo-electron tomography studies that have begun to unravel a wide spectrum of molecular architectures, ranging from amorphous to crystalline assemblies, that underlie cellular condensates. These observations bring into question current interpretations of microscopic phase behavior. Furthermore, by examining emerging concepts of non-classical phase separation pathways in small-molecule crystallization, we draw parallels with biomolecular condensation that highlight aspects not yet fully explored. In particular, transient and metastable intermediates that might be challenging to capture experimentally inside cells could be probed through computational simulations and enable a multi-scale understanding of the subcellular organization governed by distinct phases.
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Affiliation(s)
- Sara Kathrin Goetz
- Structural and Computational Biology Unit, European Molecular Biology Laboratory (EMBL), Meyerhofstrasse 1, 69117 Heidelberg, Germany; Collaboration for Joint PhD Degree between EMBL and Heidelberg University, Faculty of Biosciences, Im Neuenheimer Feld 234, 69120 Heidelberg, Germany
| | - Julia Mahamid
- Structural and Computational Biology Unit, European Molecular Biology Laboratory (EMBL), Meyerhofstrasse 1, 69117 Heidelberg, Germany.
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Joseph JA, Espinosa JR, Sanchez-Burgos I, Garaizar A, Frenkel D, Collepardo-Guevara R. Thermodynamics and kinetics of phase separation of protein-RNA mixtures by a minimal model. Biophys J 2021; 120:1219-1230. [PMID: 33571491 DOI: 10.1016/j.bpj.2021.01.031] [Citation(s) in RCA: 38] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Revised: 11/11/2020] [Accepted: 01/20/2021] [Indexed: 12/20/2022] Open
Abstract
Intracellular liquid-liquid phase separation enables the formation of biomolecular condensates, such as ribonucleoprotein granules, which play a crucial role in the spatiotemporal organization of biomolecules (e.g., proteins and RNAs). Here, we introduce a patchy-particle polymer model to investigate liquid-liquid phase separation of protein-RNA mixtures. We demonstrate that at low to moderate concentrations, RNA enhances the stability of RNA-binding protein condensates because it increases the molecular connectivity of the condensed-liquid phase. Importantly, we find that RNA can also accelerate the nucleation stage of phase separation. Additionally, we assess how the capacity of RNA to increase the stability of condensates is modulated by the relative protein-protein/protein-RNA binding strengths. We find that phase separation and multiphase organization of multicomponent condensates is favored when the RNA binds with higher affinity to the lower-valency proteins in the mixture than to the cognate higher-valency proteins. Collectively, our results shed light on the roles of RNA in ribonucleoprotein granule formation and the internal structuring of stress granules.
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Affiliation(s)
- Jerelle A Joseph
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, United Kingdom; Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom; Department of Genetics, University of Cambridge, Cambridge, United Kingdom
| | - Jorge R Espinosa
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, United Kingdom; Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom; Department of Genetics, University of Cambridge, Cambridge, United Kingdom
| | - Ignacio Sanchez-Burgos
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, United Kingdom; Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom; Department of Genetics, University of Cambridge, Cambridge, United Kingdom
| | - Adiran Garaizar
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, United Kingdom; Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom; Department of Genetics, University of Cambridge, Cambridge, United Kingdom
| | - Daan Frenkel
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
| | - Rosana Collepardo-Guevara
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, United Kingdom; Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom; Department of Genetics, University of Cambridge, Cambridge, United Kingdom.
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Das S, Lin YH, Vernon RM, Forman-Kay JD, Chan HS. Comparative roles of charge, π, and hydrophobic interactions in sequence-dependent phase separation of intrinsically disordered proteins. Proc Natl Acad Sci U S A 2020; 117:28795-28805. [PMID: 33139563 PMCID: PMC7682375 DOI: 10.1073/pnas.2008122117] [Citation(s) in RCA: 131] [Impact Index Per Article: 32.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
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.
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Affiliation(s)
- Suman Das
- Department of Biochemistry, University of Toronto, Toronto, ON M5S 1A8, Canada
| | - Yi-Hsuan Lin
- Department of Biochemistry, University of Toronto, Toronto, ON M5S 1A8, Canada
- Molecular Medicine, Hospital for Sick Children, Toronto, ON M5G 0A4, Canada
| | - Robert M Vernon
- Molecular Medicine, Hospital for Sick Children, Toronto, ON M5G 0A4, Canada
| | - Julie D Forman-Kay
- Molecular Medicine, Hospital for Sick Children, Toronto, ON M5G 0A4, Canada
- Department of Biochemistry, University of Toronto, Toronto, ON M5S 1A8, Canada
| | - Hue Sun Chan
- Department of Biochemistry, University of Toronto, Toronto, ON M5S 1A8, Canada;
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