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Zhou HX, Kota D, Qin S, Prasad R. Fundamental Aspects of Phase-Separated Biomolecular Condensates. Chem Rev 2024; 124:8550-8595. [PMID: 38885177 PMCID: PMC11260227 DOI: 10.1021/acs.chemrev.4c00138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/20/2024]
Abstract
Biomolecular condensates, formed through phase separation, are upending our understanding in much of molecular, cell, and developmental biology. There is an urgent need to elucidate the physicochemical foundations of the behaviors and properties of biomolecular condensates. Here we aim to fill this need by writing a comprehensive, critical, and accessible review on the fundamental aspects of phase-separated biomolecular condensates. We introduce the relevant theoretical background, present the theoretical basis for the computation and experimental measurement of condensate properties, and give mechanistic interpretations of condensate behaviors and properties in terms of interactions at the molecular and residue levels.
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Affiliation(s)
- Huan-Xiang Zhou
- Department of Chemistry, University of Illinois Chicago, Chicago, Illinois 60607, USA
- Department of Physics, University of Illinois Chicago, Chicago, Illinois 60607, USA
| | - Divya Kota
- Department of Chemistry, University of Illinois Chicago, Chicago, Illinois 60607, USA
| | - Sanbo Qin
- Department of Chemistry, University of Illinois Chicago, Chicago, Illinois 60607, USA
| | - Ramesh Prasad
- Department of Chemistry, University of Illinois Chicago, Chicago, Illinois 60607, USA
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2
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Kwon S, Pantelopulos GA, Straub JE. Efficient calculation of the free energy for protein partitioning using restraining potentials. Biophys J 2023; 122:1914-1925. [PMID: 35962549 PMCID: PMC10257010 DOI: 10.1016/j.bpj.2022.07.031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 07/14/2022] [Accepted: 07/25/2022] [Indexed: 11/29/2022] Open
Abstract
An approach for the efficient simulation of phase-separated lipid bilayers, for use in the calculation of equilibrium free energies of partitioning between lipid domains, is proposed. The methodology exploits restraint potentials and rectangular aspect ratios that enforce lipid phase separation, allowing for the simulation of smaller systems that approximately reproduce bulk behavior. The utility of this approach is demonstrated through the calculation of potentials of mean force for the translation of a transmembrane protein between lipid domains. The impact of the imposed restraints on lipid tail ordering and lipid packing are explored, providing insight into how restraints can best be employed to compute accurate free-energy surfaces. This approach should be useful in the accurate calculation of equilibrium partition coefficients for transmembrane protein partitioning in heterogeneous membranes, providing insight into the thermodynamic driving forces that control this fundamental biophysical phenomenon.
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Affiliation(s)
- Seulki Kwon
- Department of Chemistry, Boston University, Boston, Massachusetts
| | - George A Pantelopulos
- Department of Chemistry, Boston University, Boston, Massachusetts; Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland
| | - John E Straub
- Department of Chemistry, Boston University, Boston, Massachusetts.
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3
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Rekhi S, Sundaravadivelu Devarajan D, Howard MP, Kim YC, Nikoubashman A, Mittal J. Role of Strong Localized vs Weak Distributed Interactions in Disordered Protein Phase Separation. J Phys Chem B 2023; 127:3829-3838. [PMID: 37079924 PMCID: PMC10187732 DOI: 10.1021/acs.jpcb.3c00830] [Citation(s) in RCA: 16] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2023] [Revised: 04/03/2023] [Indexed: 04/22/2023]
Abstract
Interaction strength and localization are critical parameters controlling the single-chain and condensed-state properties of intrinsically disordered proteins (IDPs). Here, we decipher these relationships using coarse-grained heteropolymers comprised of hydrophobic (H) and polar (P) monomers as model IDPs. We systematically vary the fraction of P monomers XP and employ two distinct particle-based models that include either strong localized attractions between only H-H pairs (HP model) or weak distributed attractions between both H-H and H-P pairs (HP+ model). To compare different sequences and models, we first carefully tune the attraction strength for all sequences to match the single-chain radius of gyration. Interestingly, we find that this procedure produces similar conformational ensembles, nonbonded potential energies, and chain-level dynamics for single chains of almost all sequences in both models, with some deviations for the HP model at large XP. However, we observe a surprisingly rich phase behavior for the sequences in both models that deviates from the expectation that similarity at the single-chain level will translate to a similar phase-separation propensity. Coexistence between dilute and dense phases is only observed up to a model-dependent XP, despite the presence of favorable interchain interactions, which we quantify using the second virial coefficient. Instead, the limited number of attractive sites (H monomers) leads to the self-assembly of finite-sized clusters of different sizes depending on XP. Our findings strongly suggest that models with distributed interactions favor the formation of liquid-like condensates over a much larger range of sequence compositions compared to models with localized interactions.
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Affiliation(s)
- Shiv Rekhi
- Artie
McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States
| | | | - Michael P. Howard
- Department
of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States
| | - Young C. Kim
- Center
for Materials Physics and Technology, Naval
Research Laboratory, Washington, D.C. 20375, United States
| | - Arash Nikoubashman
- Institute
of Physics, Johannes Gutenberg University
Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Jeetain Mittal
- Artie
McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States
- Department
of Chemistry, Texas A&M University, College Station, Texas 77843, United States
- Interdisciplinary
Graduate Program in Genetics and Genomics, Texas A&M University, College
Station, Texas 77843, United States
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4
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Li L, Paloni M, Finney AR, Barducci A, Salvalaglio M. Nucleation of Biomolecular Condensates from Finite-Sized Simulations. J Phys Chem Lett 2023; 14:1748-1755. [PMID: 36758221 PMCID: PMC9940850 DOI: 10.1021/acs.jpclett.2c03512] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Accepted: 01/30/2023] [Indexed: 06/18/2023]
Abstract
The nucleation of protein condensates is a concentration-driven process of assembly. When modeled in the canonical ensemble, condensation is affected by finite-size effects. Here, we present a general and efficient route for obtaining ensemble properties of protein condensates in the macroscopic limit from finite-sized nucleation simulations. The approach is based on a theoretical description of droplet nucleation in the canonical ensemble and enables estimation of thermodynamic and kinetic parameters, such as the macroscopic equilibrium density of the dilute protein phase, the surface tension of the condensates, and nucleation free energy barriers. We apply the method to coarse-grained simulations of NDDX4 and FUS-LC, two phase-separating disordered proteins with different physicochemical characteristics. Our results show that NDDX4 condensate droplets, characterized by lower surface tension, higher solubility, and faster monomer exchange dynamics compared to those of FUS-LC, form with negligible nucleation barriers. In contrast, FUS-LC condensates form via an activated process over a wide range of concentrations.
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Affiliation(s)
- Lunna Li
- Thomas
Young Centre and Department of Chemical Engineering, University College London, London WC1E 7JE, U.K.
| | - Matteo Paloni
- Université
de Montpellier, Centre de Biologie Structurale
(CBS), CNRS, INSERM, 34090 Montpellier, France
| | - Aaron R. Finney
- Thomas
Young Centre and Department of Chemical Engineering, University College London, London WC1E 7JE, U.K.
| | - Alessandro Barducci
- Université
de Montpellier, Centre de Biologie Structurale
(CBS), CNRS, INSERM, 34090 Montpellier, France
| | - Matteo Salvalaglio
- Thomas
Young Centre and Department of Chemical Engineering, University College London, London WC1E 7JE, U.K.
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5
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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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6
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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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7
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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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Rana U, Brangwynne CP, Panagiotopoulos AZ. Phase separation vs aggregation behavior for model disordered proteins. J Chem Phys 2021; 155:125101. [PMID: 34598580 DOI: 10.1063/5.0060046] [Citation(s) in RCA: 33] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Liquid-liquid phase separation (LLPS) is widely utilized by the cell to organize and regulate various biochemical processes. Although the LLPS of proteins is known to occur in a sequence-dependent manner, it is unclear how sequence properties dictate the nature of the phase transition and thereby influence condensed phase morphology. In this work, we have utilized grand canonical Monte Carlo simulations for a simple coarse-grained model of disordered proteins to systematically investigate how sequence distribution, sticker fraction, and chain length impact the formation of finite-size aggregates, which can preempt macroscopic phase separation for some sequences. We demonstrate that a normalized sequence charge decoration (SCD) parameter establishes a "soft" predictive criterion for distinguishing when a model protein undergoes macroscopic phase separation vs finite aggregation. Additionally, we find that this order parameter is strongly correlated with the critical density for phase separation, highlighting an unambiguous connection between sequence distribution and condensed phase density. Results obtained from an analysis of the order parameter reveal that at sufficiently long chain lengths, the vast majority of sequences are likely to phase separate. Our results suggest that classical LLPS should be the primary phase transition for disordered proteins when short-ranged attractive interactions dominate and suggest a possible reason behind recent findings of widespread phase separation throughout living cells.
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Affiliation(s)
- Ushnish Rana
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Clifford P Brangwynne
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
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