101
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Matsubara D, Kasahara K, Dokainish HM, Oshima H, Sugita Y. Modified Protein-Water Interactions in CHARMM36m for Thermodynamics and Kinetics of Proteins in Dilute and Crowded Solutions. Molecules 2022; 27:molecules27175726. [PMID: 36080494 PMCID: PMC9457699 DOI: 10.3390/molecules27175726] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2022] [Revised: 08/30/2022] [Accepted: 08/30/2022] [Indexed: 11/16/2022] Open
Abstract
Proper balance between protein-protein and protein-water interactions is vital for atomistic molecular dynamics (MD) simulations of globular proteins as well as intrinsically disordered proteins (IDPs). The overestimation of protein-protein interactions tends to make IDPs more compact than those in experiments. Likewise, multiple proteins in crowded solutions are aggregated with each other too strongly. To optimize the balance, Lennard-Jones (LJ) interactions between protein and water are often increased about 10% (with a scaling parameter, λ = 1.1) from the existing force fields. Here, we explore the optimal scaling parameter of protein-water LJ interactions for CHARMM36m in conjunction with the modified TIP3P water model, by performing enhanced sampling MD simulations of several peptides in dilute solutions and conventional MD simulations of globular proteins in dilute and crowded solutions. In our simulations, 10% increase of protein-water LJ interaction for the CHARMM36m cannot maintain stability of a small helical peptide, (AAQAA)3 in a dilute solution and only a small modification of protein-water LJ interaction up to the 3% increase (λ = 1.03) is allowed. The modified protein-water interactions are applicable to other peptides and globular proteins in dilute solutions without changing thermodynamic properties from the original CHARMM36m. However, it has a great impact on the diffusive properties of proteins in crowded solutions, avoiding the formation of too sticky protein-protein interactions.
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Affiliation(s)
- Daiki Matsubara
- Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, Kobe 650-0047, Hyogo, Japan
| | - Kento Kasahara
- Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, Kobe 650-0047, Hyogo, Japan
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Osaka, Japan
| | - Hisham M. Dokainish
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, Wako 351-0198, Saitama, Japan
| | - Hiraku Oshima
- Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, Kobe 650-0047, Hyogo, Japan
| | - Yuji Sugita
- Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, Kobe 650-0047, Hyogo, Japan
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, Wako 351-0198, Saitama, Japan
- Computational Biophysics Research Team, RIKEN Center for Computational Science, Kobe 650-0047, Hyogo, Japan
- Correspondence: ; Tel.: +81-48-462-1407
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102
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Michieletto D, Marenda M. Rheology and Viscoelasticity of Proteins and Nucleic Acids Condensates. JACS AU 2022; 2:1506-1521. [PMID: 35911447 PMCID: PMC9326828 DOI: 10.1021/jacsau.2c00055] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Phase separation is as familiar as watching vinegar separating from oil in vinaigrette. The observation that phase separation of proteins and nucleic acids is widespread in living cells has opened an entire field of research into the biological significance and the biophysical mechanisms of phase separation and protein condensation in biology. Recent evidence indicates that certain proteins and nucleic acids condensates are not simple liquids and instead display both viscous and elastic behaviors, which in turn may have biological significance. The aim of this Perspective is to review the state-of-the-art of this quickly emerging field focusing on the material and rheological properties of protein condensates. Finally, we discuss the different techniques that can be employed to quantify the viscoelasticity of condensates and highlight potential future directions and opportunities for interdisciplinary cross-talk between chemists, physicists, and biologists.
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Affiliation(s)
- Davide Michieletto
- School
of Physics and Astronomy, University of
Edinburgh, Peter Guthrie
Tait Road, Edinburgh EH9
3FD, U.K.
- MRC
Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh EH4 2XU, U.K.
| | - Mattia Marenda
- School
of Physics and Astronomy, University of
Edinburgh, Peter Guthrie
Tait Road, Edinburgh EH9
3FD, U.K.
- MRC
Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh EH4 2XU, U.K.
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103
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Garaizar A, Espinosa JR, Joseph JA, Krainer G, Shen Y, Knowles TP, Collepardo-Guevara R. Aging can transform single-component protein condensates into multiphase architectures. Proc Natl Acad Sci U S A 2022; 119:e2119800119. [PMID: 35727989 PMCID: PMC9245653 DOI: 10.1073/pnas.2119800119] [Citation(s) in RCA: 27] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Accepted: 03/28/2022] [Indexed: 01/23/2023] Open
Abstract
Phase-separated biomolecular condensates that contain multiple coexisting phases are widespread in vitro and in cells. Multiphase condensates emerge readily within multicomponent mixtures of biomolecules (e.g., proteins and nucleic acids) when the different components present sufficient physicochemical diversity (e.g., in intermolecular forces, structure, and chemical composition) to sustain separate coexisting phases. Because such diversity is highly coupled to the solution conditions (e.g., temperature, pH, salt, composition), it can manifest itself immediately from the nucleation and growth stages of condensate formation, develop spontaneously due to external stimuli or emerge progressively as the condensates age. Here, we investigate thermodynamic factors that can explain the progressive intrinsic transformation of single-component condensates into multiphase architectures during the nonequilibrium process of aging. We develop a multiscale model that integrates atomistic simulations of proteins, sequence-dependent coarse-grained simulations of condensates, and a minimal model of dynamically aging condensates with nonconservative intermolecular forces. Our nonequilibrium simulations of condensate aging predict that single-component condensates that are initially homogeneous and liquid like can transform into gel-core/liquid-shell or liquid-core/gel-shell multiphase condensates as they age due to gradual and irreversible enhancement of interprotein interactions. The type of multiphase architecture is determined by the aging mechanism, the molecular organization of the gel and liquid phases, and the chemical makeup of the protein. Notably, we predict that interprotein disorder to order transitions within the prion-like domains of intracellular proteins can lead to the required nonconservative enhancement of intermolecular interactions. Our study, therefore, predicts a potential mechanism by which the nonequilibrium process of aging results in single-component multiphase condensates.
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Affiliation(s)
- Adiran Garaizar
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - Jorge R. Espinosa
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - Jerelle A. Joseph
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
- Department of Genetics, University of Cambridge, Cambridge CB2 3EH, United Kingdom
| | - Georg Krainer
- Centre for Misfolding Diseases, Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Yi Shen
- School of Chemical and Biomolecular Engineering, The University of Sydney, Sydney, NSW 2006, Australia
- The University of Sydney Nano Institute, The University of Sydney, Sydney, NSW 2006, Australia
| | - Tuomas P.J. Knowles
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom
- Centre for Misfolding Diseases, Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Rosana Collepardo-Guevara
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
- Department of Genetics, University of Cambridge, Cambridge CB2 3EH, United Kingdom
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104
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Gueta O, Sheinenzon O, Azulay R, Shalit H, Strugach DS, Hadar D, Gelkop S, Milo A, Amiram M. Tuning the Properties of Protein-Based Polymers Using High-Performance Orthogonal Translation Systems for the Incorporation of Aromatic Non-Canonical Amino Acids. Front Bioeng Biotechnol 2022; 10:913057. [PMID: 35711629 PMCID: PMC9195583 DOI: 10.3389/fbioe.2022.913057] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2022] [Accepted: 04/27/2022] [Indexed: 12/28/2022] Open
Abstract
The incorporation of non-canonical amino acids (ncAAs) using engineered aminoacyl-tRNA synthetases (aaRSs) has emerged as a powerful methodology to expand the chemical repertoire of proteins. However, the low efficiencies of typical aaRS variants limit the incorporation of ncAAs to only one or a few sites within a protein chain, hindering the design of protein-based polymers (PBPs) in which multi-site ncAA incorporation can be used to impart new properties and functions. Here, we determined the substrate specificities of 11 recently developed high-performance aaRS variants and identified those that enable an efficient multi-site incorporation of 15 different aromatic ncAAs. We used these aaRS variants to produce libraries of two temperature-responsive PBPs—elastin- and resilin-like polypeptides (ELPs and RLPs, respectively)—that bear multiple instances of each ncAA. We show that incorporating such aromatic ncAAs into the protein structure of ELPs and RLPs can affect their temperature responsiveness, secondary structure, and self-assembly propensity, yielding new and diverse families of ELPs and RLPs, each from a single DNA template. Finally, using a molecular model, we demonstrate that the temperature-responsive behavior of RLPs is strongly affected by both the hydrophobicity and the size of the unnatural aromatic side-chain. The ability to efficiently incorporate multiple instances of diverse ncAAs alongside the 20 natural amino acids can help to elucidate the effect of ncAA incorporation on these and many other PBPs, with the aim of designing additional precise and chemically diverse polymers with new or improved properties.
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Affiliation(s)
- Osher Gueta
- Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben-Gurion University of the Negev, Beersheba, Israel
| | - Ortal Sheinenzon
- Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben-Gurion University of the Negev, Beersheba, Israel
| | - Rotem Azulay
- Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben-Gurion University of the Negev, Beersheba, Israel
| | - Hadas Shalit
- Department of Chemistry, Ben-Gurion University of the Negev, Beersheba, Israel
| | - Daniela S Strugach
- Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben-Gurion University of the Negev, Beersheba, Israel
| | - Dagan Hadar
- Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben-Gurion University of the Negev, Beersheba, Israel
| | - Sigal Gelkop
- Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben-Gurion University of the Negev, Beersheba, Israel
| | - Anat Milo
- Department of Chemistry, Ben-Gurion University of the Negev, Beersheba, Israel
| | - Miriam Amiram
- Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben-Gurion University of the Negev, Beersheba, Israel
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105
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Huertas J, Woods EJ, Collepardo-Guevara R. Multiscale modelling of chromatin organisation: Resolving nucleosomes at near-atomistic resolution inside genes. Curr Opin Cell Biol 2022; 75:102067. [DOI: 10.1016/j.ceb.2022.02.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Revised: 01/24/2022] [Accepted: 02/04/2022] [Indexed: 12/15/2022]
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106
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Garaizar A, Espinosa JR, Joseph JA, Collepardo-Guevara R. Kinetic interplay between droplet maturation and coalescence modulates shape of aged protein condensates. Sci Rep 2022; 12:4390. [PMID: 35293386 PMCID: PMC8924231 DOI: 10.1038/s41598-022-08130-2] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Accepted: 02/07/2022] [Indexed: 12/29/2022] Open
Abstract
Biomolecular condensates formed by the process of liquid-liquid phase separation (LLPS) play diverse roles inside cells, from spatiotemporal compartmentalisation to speeding up chemical reactions. Upon maturation, the liquid-like properties of condensates, which underpin their functions, are gradually lost, eventually giving rise to solid-like states with potential pathological implications. Enhancement of inter-protein interactions is one of the main mechanisms suggested to trigger the formation of solid-like condensates. To gain a molecular-level understanding of how the accumulation of stronger interactions among proteins inside condensates affect the kinetic and thermodynamic properties of biomolecular condensates, and their shapes over time, we develop a tailored coarse-grained model of proteins that transition from establishing weak to stronger inter-protein interactions inside condensates. Our simulations reveal that the fast accumulation of strongly binding proteins during the nucleation and growth stages of condensate formation results in aspherical solid-like condensates. In contrast, when strong inter-protein interactions appear only after the equilibrium condensate has been formed, or when they accumulate slowly over time with respect to the time needed for droplets to fuse and grow, spherical solid-like droplets emerge. By conducting atomistic potential-of-mean-force simulations of NUP-98 peptides-prone to forming inter-protein [Formula: see text]-sheets-we observe that formation of inter-peptide [Formula: see text]-sheets increases the strength of the interactions consistently with the loss of liquid-like condensate properties we observe at the coarse-grained level. Overall, our work aids in elucidating fundamental molecular, kinetic, and thermodynamic mechanisms linking the rate of change in protein interaction strength to condensate shape and maturation during ageing.
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Affiliation(s)
- Adiran Garaizar
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge, CB3 0HE, UK
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
| | - Jorge R Espinosa
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge, CB3 0HE, UK
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
| | - Jerelle A Joseph
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge, CB3 0HE, UK
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
- Department of Genetics, University of Cambridge, Downing Site, Cambridge, CB2 3EH, UK
| | - Rosana Collepardo-Guevara
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge, CB3 0HE, UK.
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.
- Department of Genetics, University of Cambridge, Downing Site, Cambridge, CB2 3EH, UK.
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107
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Sanchez-Burgos I, Espinosa JR, Joseph JA, Collepardo-Guevara R. RNA length has a non-trivial effect in the stability of biomolecular condensates formed by RNA-binding proteins. PLoS Comput Biol 2022; 18:e1009810. [PMID: 35108264 PMCID: PMC8896709 DOI: 10.1371/journal.pcbi.1009810] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Revised: 03/04/2022] [Accepted: 01/06/2022] [Indexed: 12/29/2022] Open
Abstract
Biomolecular condensates formed via liquid-liquid phase separation (LLPS) play a crucial role in the spatiotemporal organization of the cell material. Nucleic acids can act as critical modulators in the stability of these protein condensates. To unveil the role of RNA length in regulating the stability of RNA binding protein (RBP) condensates, we present a multiscale computational strategy that exploits the advantages of a sequence-dependent coarse-grained representation of proteins and a minimal coarse-grained model wherein proteins are described as patchy colloids. We find that for a constant nucleotide/protein ratio, the protein fused in sarcoma (FUS), which can phase separate on its own-i.e., via homotypic interactions-only exhibits a mild dependency on the RNA strand length. In contrast, the 25-repeat proline-arginine peptide (PR25), which does not undergo LLPS on its own at physiological conditions but instead exhibits complex coacervation with RNA-i.e., via heterotypic interactions-shows a strong dependence on the length of the RNA strands. Our minimal patchy particle simulations suggest that the strikingly different effect of RNA length on homotypic LLPS versus RBP-RNA complex coacervation is general. Phase separation is RNA-length dependent whenever the relative contribution of heterotypic interactions sustaining LLPS is comparable or higher than those stemming from protein homotypic interactions. Taken together, our results contribute to illuminate the intricate physicochemical mechanisms that influence the stability of RBP condensates through RNA inclusion.
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Affiliation(s)
- Ignacio Sanchez-Burgos
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge, United Kingdom
| | - Jorge R. Espinosa
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge, United Kingdom
| | - Jerelle A. Joseph
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge, United Kingdom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, United Kingdom
- Department of Genetics, University of Cambridge, Downing Site, Cambridge, United Kingdom
| | - Rosana Collepardo-Guevara
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge, United Kingdom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, United Kingdom
- Department of Genetics, University of Cambridge, Downing Site, Cambridge, United Kingdom
- * E-mail:
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108
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Tejedor AR, Garaizar A, Ramírez J, Espinosa JR. 'RNA modulation of transport properties and stability in phase-separated condensates. Biophys J 2021; 120:5169-5186. [PMID: 34762868 DOI: 10.1101/2021.03.05.434111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Revised: 09/03/2021] [Accepted: 10/03/2021] [Indexed: 05/25/2023] Open
Abstract
One of the key mechanisms employed by cells to control their spatiotemporal organization is the formation and dissolution of phase-separated condensates. The balance between condensate assembly and disassembly can be critically regulated by the presence of RNA. In this work, we use a chemically-accurate sequence-dependent coarse-grained model for proteins and RNA to unravel the impact of RNA in modulating the transport properties and stability of biomolecular condensates. We explore the phase behavior of several RNA-binding proteins such as FUS, hnRNPA1, and TDP-43 proteins along with that of their corresponding prion-like domains and RNA recognition motifs from absence to moderately high RNA concentration. By characterizing the phase diagram, key molecular interactions, surface tension, and transport properties of the condensates, we report a dual RNA-induced behavior: on the one hand, RNA enhances phase separation at low concentration as long as the RNA radius of gyration is comparable to that of the proteins, whereas at high concentration, it inhibits the ability of proteins to self-assemble independently of its length. On the other hand, along with the stability modulation, the viscosity of the condensates can be considerably reduced at high RNA concentration as long as the length of the RNA chains is shorter than that of the proteins. Conversely, long RNA strands increase viscosity even at high concentration, but barely modify protein self-diffusion which mainly depends on RNA concentration and on the effect RNA has on droplet density. On the whole, our work rationalizes the different routes by which RNA can regulate phase separation and condensate dynamics, as well as the subsequent aberrant rigidification implicated in the emergence of various neuropathologies and age-related diseases.
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Affiliation(s)
- Andrés R Tejedor
- Department of Chemical Engineering, Universidad Politécnica de Madrid, Madrid, Spain
| | - Adiran Garaizar
- Cavendish Laboratory, Maxwell Centre, Department of Physics, University of Cambridge, Cambridge, United Kingdom
| | - Jorge Ramírez
- Department of Chemical Engineering, Universidad Politécnica de Madrid, Madrid, Spain.
| | - Jorge R Espinosa
- Cavendish Laboratory, Maxwell Centre, Department of Physics, University of Cambridge, Cambridge, United Kingdom.
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109
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Tejedor AR, Garaizar A, Ramírez J, Espinosa JR. 'RNA modulation of transport properties and stability in phase-separated condensates. Biophys J 2021; 120:5169-5186. [PMID: 34762868 PMCID: PMC8715277 DOI: 10.1016/j.bpj.2021.11.003] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Revised: 09/03/2021] [Accepted: 10/03/2021] [Indexed: 12/29/2022] Open
Abstract
One of the key mechanisms employed by cells to control their spatiotemporal organization is the formation and dissolution of phase-separated condensates. The balance between condensate assembly and disassembly can be critically regulated by the presence of RNA. In this work, we use a chemically-accurate sequence-dependent coarse-grained model for proteins and RNA to unravel the impact of RNA in modulating the transport properties and stability of biomolecular condensates. We explore the phase behavior of several RNA-binding proteins such as FUS, hnRNPA1, and TDP-43 proteins along with that of their corresponding prion-like domains and RNA recognition motifs from absence to moderately high RNA concentration. By characterizing the phase diagram, key molecular interactions, surface tension, and transport properties of the condensates, we report a dual RNA-induced behavior: on the one hand, RNA enhances phase separation at low concentration as long as the RNA radius of gyration is comparable to that of the proteins, whereas at high concentration, it inhibits the ability of proteins to self-assemble independently of its length. On the other hand, along with the stability modulation, the viscosity of the condensates can be considerably reduced at high RNA concentration as long as the length of the RNA chains is shorter than that of the proteins. Conversely, long RNA strands increase viscosity even at high concentration, but barely modify protein self-diffusion which mainly depends on RNA concentration and on the effect RNA has on droplet density. On the whole, our work rationalizes the different routes by which RNA can regulate phase separation and condensate dynamics, as well as the subsequent aberrant rigidification implicated in the emergence of various neuropathologies and age-related diseases.
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Affiliation(s)
- Andrés R Tejedor
- Department of Chemical Engineering, Universidad Politécnica de Madrid, Madrid, Spain
| | - Adiran Garaizar
- Cavendish Laboratory, Maxwell Centre, Department of Physics, University of Cambridge, Cambridge, United Kingdom
| | - Jorge Ramírez
- Department of Chemical Engineering, Universidad Politécnica de Madrid, Madrid, Spain.
| | - Jorge R Espinosa
- Cavendish Laboratory, Maxwell Centre, Department of Physics, University of Cambridge, Cambridge, United Kingdom.
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