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Biophysics Reports 2022, 8(2): 55-67 https://doi.org/10.52601/bpr.2022.210029
Protocol | Open Access | Issue | Published: 25 March 2022

Theoretical modelling of liquid–liquid phase separation: from particle-based to field-based simulation

Show Author's Information Lin-ge Li1,  Zhonghuai Hou1( )
Hefei National Laboratory for Physical Sciences at the Microscale & Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China
Keywords:
Liquid–liquid phase separation, Theoretical modelling, Coarse-grained simulation
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Li L-g, Hou Z. Theoretical modelling of liquid–liquid phase separation: from particle-based to field-based simulation. Biophysics Reports, 2022, 8(2): 55-67. https://doi.org/10.52601/bpr.2022.210029
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Abstract Full text About this article

Liquid–liquid phase separation (LLPS) has proved to be ubiquitous in living cells, forming membraneless organelles (MLOs) and dynamic condensations essential in physiological processes. However, some underlying mechanisms remain challenging to unravel experimentally, making theoretical modeling an indispensable aspect. Here we present a protocol for understanding LLPS from fundamental physics to detailed modeling procedures. The protocol involves a comprehensive physical picture on selecting suitable theoretical approaches, as well as how and what to interpret and resolve from the results. On the particle-based level, we elaborate on coarse-grained simulation procedures from building up models, identifying crucial interactions to running simulations to obtain phase diagrams and other concerned properties. We also outline field-based theories which give the system's density profile to determine phase diagrams and provide dynamic properties by studying the time evolution of density field, enabling us to characterize LLPS systems with larger time and length scales and to further include other nonequilibrium factors such as chemical reactions.


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About this article

Theoretical modelling of liquid–liquid phase separation: from particle-based to field-based simulation

Show Author's information Lin-ge Li1, Zhonghuai Hou1( )
Hefei National Laboratory for Physical Sciences at the Microscale & Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China

Abstract

Liquid–liquid phase separation (LLPS) has proved to be ubiquitous in living cells, forming membraneless organelles (MLOs) and dynamic condensations essential in physiological processes. However, some underlying mechanisms remain challenging to unravel experimentally, making theoretical modeling an indispensable aspect. Here we present a protocol for understanding LLPS from fundamental physics to detailed modeling procedures. The protocol involves a comprehensive physical picture on selecting suitable theoretical approaches, as well as how and what to interpret and resolve from the results. On the particle-based level, we elaborate on coarse-grained simulation procedures from building up models, identifying crucial interactions to running simulations to obtain phase diagrams and other concerned properties. We also outline field-based theories which give the system's density profile to determine phase diagrams and provide dynamic properties by studying the time evolution of density field, enabling us to characterize LLPS systems with larger time and length scales and to further include other nonequilibrium factors such as chemical reactions.

Keywords: Liquid–liquid phase separation, Theoretical modelling, Coarse-grained simulation

References(62)

Alshareedah I, Moosa MM, Raju M, Potoyan DA, Banerjee PR (2020) Phase transition of RNA−protein complexes into ordered hollow condensates. Proc Natl Acad Sci USA 117(27): 15650−15658
DOI Google Scholar

Ando T, Skolnick J (2010) Crowding and hydrodynamic interactions likely dominate in vivo macromolecular motion. Proc Natl Acad Sci USA 107(43): 18457−18462
DOI Google Scholar

André AAM, Spruijt E (2020) Liquid–liquid phase separation in crowded environments. Int J Mol Sci 21(16): 5908. https://doi.org/10.3390/ijms21165908
DOI Google Scholar

Berendsen HJC, van der Spoel D, van Drunen R (1995) GROMACS: a message-passing parallel molecular dynamics implementation. Comp Phys Commun 91: 43−56
DOI Google Scholar

Bianchi E, Blaak R, Likos CN (2011) Patchy colloids: state of the art and perspectives. Phys Chem Chem Phys 13: 6397−6410
DOI Google Scholar

Boeynaems S, Alberti S, Fawzi NL, Mittag T, Polymenidou M, Rousseau F, Schymkowitz J, Shorter J, Wolozin B, Van Den Bosch L, Tompa P, Fuxreiter M (2018) Protein phase separation: a new phase in cell biology. Trends Cell Biol 28(6): 420−435
DOI Google Scholar

Borukhov S, Lee J, Laptenko O (2005) Bacterial transcription elongation factors: new insights into molecular mechanism of action. Mol Microbiol 55(5): 1315−1324
DOI Google Scholar

Bracha D, Walls MT, Wei M-T, Zhu L, Kurian M, Avalos JL, Toettcher JE, Brangwynne CP (2019) Mapping local and global liquid phase behavior in living cells using photo-oligomerizable seeds. Cell 176(1-2): 407. https://doi.org/10.1016/j.cell.2018.12.026
DOI Google Scholar

Brangwynne CP, Eckmann CR, Courson DS, Rybarska A, Hoege C, Gharakhani J, Jülicher F, Hyman AA (2009) Germline P granules are liquid droplets that localize by controlled dissolution/condensation. Science 324(5935): 1729−1732
DOI Google Scholar

Brangwynne CP, Mitchison TJ, Hyman AA (2011) Active liquid-like behavior of nucleoli determines their size and shape in Xenopus laevis oocytes. Proc Natl Acad Sci 108(11): 4334−4339
DOI Google Scholar

Brangwynne Clifford P, Tompa P, Pappu Rohit V (2015) Polymer physics of intracellular phase transitions. Nat Phys 11(11): 899−904
DOI Google Scholar

Burke KA, Janke AM, Rhine CL, Fawzi NL (2015) Residue-by-residue view of in vitro FUS granules that bind the C-terminal domain of RNA polymerase II. Mol Cell 60: 231−241
DOI Google Scholar

Chang L-W, Lytle TK, Radhakrishna M, Madinya JJ, Vélez J, Sing CE, Perry SL (2017) Sequence and entropy-based control of complex coacervates. Nat Commun 8(1): 1273. https://doi.org/10.1038/s41467-017-01249-1
DOI Google Scholar

Choi J-M, Dar F, Pappu RV (2019) LASSI: a lattice model for simulating phase transitions of multivalent proteins. PLoS Comput Biol 15(10): e1007028. https://doi.org/10.1371/journal.pcbi.1007028
DOI Google Scholar

Conicella AE, Zerze GH, Mittal J, Fawzi NL (2016) ALS mutations disrupt phase separation mediated by α-helical structure in the TDP-43 low-complexity C-terminal domain. Structure 24: 1537−1549
DOI Google Scholar

Dannenhoffer-Lafage T, Best RB (2021) A data-driven hydrophobicity scale for predicting liquid–liquid phase separation of proteins. J Phys Chem B 125(16): 4046−4056
DOI Google Scholar

Das S, Amin AN, Lin Y-H, Chan HS (2018a) Coarse-grained residue-based models of disordered protein condensates: utility and limitations of simple charge pattern parameters. Phys Chem Chem Phys 20: 28558−28574
DOI Google Scholar

Das S, Eisen A, Lin Y-H, Chan HS (2018b) A lattice model of charge-pattern-dependent polyampholyte phase separation. J Phys Chem B 122: 5418−5431
DOI Google Scholar

Dignon GL, Zheng W, Kim YC, Best RB, Mittal J (2018) Sequence determinants of protein phase behavior from a coarse-grained model. PLoS Comput Biol 14(1): e1005941. https://doi.org/10.1371/journal.pcbi.1005941
DOI Google Scholar

Du Y, Jiang H, Hou Z (2019a) Self-assembly of active core corona particles into highly ordered and self-healing structures. J Chem Phys 151(15): 154904. https://doi.org/10.1063/1.5121802
DOI Google Scholar

Du Y, Jiang H, Hou Z (2019b) Study of active Brownian particle diffusion in polymer solutions. Soft Matter 15(9): 2020−2031
DOI Google Scholar

Falk M, Feodorova Y, Naumova N, Imakaev M, Lajoie BR, Leonhardt H, Joffe B, Dekker J, Fudenberg G, Solovei I, Mirny LA (2019) Heterochromatin drives compartmentalization of inverted and conventional nuclei. Nature 570: 395−399
DOI Google Scholar

Flory PJ (1942) Thermodynamics of high polymer solutions. J Chem Phys 10: 51−61
DOI Google Scholar

Gasior K, Zhao J, McLaughlin G, Forest MG, Gladfelter AS, Newby J (2019) Partial demixing of RNA-protein complexes leads to intradroplet patterning in phase-separated biological condensates. Phys Rev E 99(1-1): 012411. https://doi.org/10.1103/PhysRevE.99.012411
DOI Google Scholar

Gou Y-l, Jiang H-j, Hou Z-h (2021) Emergent swarming states in active particles system with opposite anisotropic interactions. Chin J Chem Phys 33(6): 717. https://doi.org/10.1063/1674-0068/cjcp2003037
DOI Google Scholar

Guillén-Boixet J, Kopach A, Holehouse AS, Wittmann S, Jahnel M, Schlüßler R, Kim K, Trussina IREA, Wang J, Mateju D (2020) RNA-induced conformational switching and clustering of G3BP drive stress granule assembly by condensation. Cell 181: 346−361
DOI Google Scholar

Henninger JE, Oksuz O, Shrinivas K, Sagi I, LeRoy G, Zheng MM, Andrews JO, Zamudio AV, Lazaris C, Hannett NM, Lee TI, Sharp PA, Cissé II, Chakraborty AK, Young RA (2021) RNA-mediated feedback control of transcriptional condensates. Cell 184: 207−225.e224
DOI Google Scholar

Hohenberg PC, Halperin BI (1977) Theory of dynamic critical phenomena. Rev Mod Phys 49: 435. https://doi.org/10.1103/RevModPhys.49.435
DOI Google Scholar

Huang DM, Chandler D (2002) The hydrophobic effect and the influence of solute−solvent attractions. J Phys Chem B 106(8): 2047−2053
DOI Google Scholar

Huggins ML (1942) Some properties of solutions of long-chain compounds. J Phys Chem 46: 151−158
DOI Google Scholar

Hyman A, Weber C, Jülicher F (2014) Liquid-liquid phase separation in biology. Annu Review Cell Dev Biol 30: 39−58
DOI Google Scholar

Jiang H, Hou Z (2014) Motion transition of active filaments: rotation without hydrodynamic interactions. Soft Matter 10(7): 1012−1017
DOI Google Scholar

Joseph JA, Espinosa JR, Sanchez-Burgos I, Garaizar A, Frenkel D, Collepardo-Guevara R (2021) Thermodynamics and kinetics of phase separation of protein-RNA mixtures by a minimal model. Biophys J 120(7): 1219−1230
DOI Google Scholar

Kapcha LH, Rossky PJ (2014) A simple atomic-level hydrophobicity scale reveals protein interfacial structure. J Mol Biol 426: 484−498
DOI Google Scholar

Kim J, Keyes T, Straub JE (2010) Generalized replica exchange method. J Chem Phys 132: 224107. https://doi.org/10.1063/1.3432176
DOI Google Scholar

Kim YC, Hummer G (2008) Coarse-grained models for simulations of multiprotein complexes: application to ubiquitin binding. J Mol Biol 375: 1416−1433
DOI Google Scholar

Kroschwald S, Maharana S, Mateju D, Malinovska L, Nüske E, Poser I, Richter D, Alberti S (2015) Promiscuous interactions and protein disaggregases determine the material state of stress-inducible RNP granules. elife 4: e06807. https://doi.org/10.7554/eLife.06807
DOI Google Scholar

Lin Y-H, Forman-Kay JD, Chan HS (2016) Sequence-specific polyampholyte phase separation in membraneless organelles. Phys Rev Lett 117(17): 178101. https://doi.org/10.1103/PhysRevLett.117.178101
DOI Google Scholar

Martin MG, Siepmann JI (1998) Transferable potentials for phase equilibria. 1. United-atom description of n-alkanes. J Phys Chem B 102: 2569−2577
DOI Google Scholar

McCarty J, Delaney KT, Danielsen SPO, Fredrickson GH, Shea J-E (2019) Complete phase diagram for liquid–liquid phase separation of intrinsically disordered proteins. J Phys Chem Lett 10: 1644−1652
DOI Google Scholar

Molliex A, Temirov J, Lee J, Coughlin M, Kanagaraj Anderson P, Kim Hong J, Mittag T, Taylor JP (2015) Phase separation by low complexity domains promotes stress granule assembly and drives pathological fibrillization. Cell 163(1): 123−133
DOI Google Scholar

Monahan Z, Ryan VH, Janke AM, Burke KA, Rhoads SN, Zerze GH, O'Meally R, Dignon GL, Conicella AE, Zheng W (2017) Phosphorylation of the FUS low‐complexity domain disrupts phase separation, aggregation, and toxicity. EMBO J 36: 2951−2967
DOI Google Scholar

Mundy CJ, Siepmann JI, Klein ML (1995) Calculation of the shear viscosity of decane using a reversible multiple time‐step algorithm. J Chem Phys 102: 3376−3380
DOI Google Scholar

Murthy AC, Dignon GL, Kan Y, Zerze GH, Parekh SH, Mittal J, Fawzi NL (2019) Molecular interactions underlying liquid−liquid phase separation of the FUS low-complexity domain. Nat Struct Mol Biol 26: 637−648
DOI Google Scholar

Needleman D, Dogic Z (2017) Active matter at the interface between materials science and cell biology. Nat Rev Mater 2(9): 17048. https://doi.org/10.1038/natrevmats.2017.48
DOI Google Scholar

Nott Timothy J, Petsalaki E, Farber P, Jervis D, Fussner E, Plochowietz A, Craggs TD, Bazett-Jones David P, Pawson T, Forman-Kay Julie D, Baldwin Andrew J (2015) Phase transition of a disordered nuage protein generates environmentally responsive membraneless organelles. Mol Cell 57: 936−947
DOI Google Scholar

Overbeek JTG, Voorn MJ (1957) Phase separation in polyelectrolyte solutions.Theory of complex coacervation. J Cell Comp Physiol 49(S1): 7−26
DOI Google Scholar

Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comp Phys 117(1): 1−19
DOI Google Scholar

Ruff KM, Pappu RV, Holehouse AS (2019) Conformational preferences and phase behavior of intrinsically disordered low complexity sequences: insights from multiscale simulations. Curr Opin Struct Biol 56: 1−10
DOI Google Scholar

Salomon-Ferrer R, Gotz AW, Poole D, Le Grand S, Walker RC (2013) Routine microsecond molecular dynamics simulations with AMBER on GPUs. 2. Explicit solvent particle mesh Ewald. J Chem Theory Comput 9: 3878−3888
DOI Google Scholar

Semenov AN, Rubinstein M (1998) Thermoreversible gelation in solutions of associative polymers.1. Statics. Macromolecules 31: 1373−1385
DOI Google Scholar

Shelley MJ (2016) The dynamics of microtubule/motor-protein assemblies in biology and physics. Annu Rev Fluid Mech 48: 487−506
DOI Google Scholar

Spoelstra WK, Jacques JM, Gonzalez-Linares R, Nobrega FL, Haagsma AC, Dogterom M, Meijer DH, Idema T, Brouns SJJ, Reese L (2021) CRISPR-based DNA and RNA detection with liquid-liquid phase separation. Biophys J 120: 1198−1209
DOI Google Scholar

Wang J, Choi J-M, Holehouse AS, Lee HO, Zhang X, Jahnel M, Maharana S, Lemaitre R, Pozniakovsky A, Drechsel D (2018) A molecular grammar governing the driving forces for phase separation of prion-like RNA binding proteins. Cell 174: 688−699
DOI Google Scholar

Wei X, Zhou J, Wang Y, Meng F (2020) Modeling elastically mediated liquid-liquid phase separation. Phys Rev Lett 125(26): 268001. https://doi.org/10.1103/PhysRevLett.125.268001
DOI Google Scholar

Wessén J, Pal T, Das S, Lin Y-H, Chan HS (2021) A simple explicit-solvent model of polyampholyte phase behaviors and its ramifications for dielectric effects in biomolecular condensates. J Phys Chem B 125: 4337−4358
DOI Google Scholar
Wright MR (2007) An introduction to aqueous electrolyte solutions. John Wiley & Sons

Zerze GlH, Best RB, Mittal J (2015) Sequence-and temperature-dependent properties of unfolded and disordered proteins from atomistic simulations. J Phys Chem B 119: 14622−14630
DOI Google Scholar

Zhang B, Wolynes PG (2015) Topology, structures, and energy landscapes of human chromosomes. Proc Natl Acad Sci USA 112(19): 6062−6067
DOI Google Scholar

Zheng W, Mittal J (2020) Using a sequence-specific coarse-grained model for studying protein liquid-liquid phase separation. Methods Enzymol 646: 1−17
DOI Google Scholar

Zwicker D, Decker M, Jaensch S, Hyman AA, Jülicher F (2014) Centrosomes are autocatalytic droplets of pericentriolar material organized by centrioles. Proc Natl Acad Sci USA 111: E2636−E2645
DOI Google Scholar

Zwicker D, Seyboldt R, Weber CA, Hyman AA, Jülicher F (2017) Growth and division of active droplets provides a model for protocells. Nat Phys 13: 408−413
DOI Google Scholar
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Publication history

Received: 28 July 2021
Accepted: 09 February 2022
Published: 25 March 2022
Issue date: April 2022

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© The Author(s) 2022

Acknowledgements

Acknowledgements

This work is supported by MOST (2018YFA0208702) and NSFC (32090040, 32090044, 21833007).

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