1
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Duque CM, Hall DM, Tyukodi B, Hagan MF, Santangelo CD, Grason GM. Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra. Proc Natl Acad Sci U S A 2024; 121:e2315648121. [PMID: 38669182 PMCID: PMC11067059 DOI: 10.1073/pnas.2315648121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 03/11/2024] [Indexed: 04/28/2024] Open
Abstract
We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.
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Affiliation(s)
- Carlos M. Duque
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden01307, Germany
- Center for Systems Biology Dresden, Dresden01307, Germany
- Department of Physics, University of Massachusetts, Amherst, MA01003
| | - Douglas M. Hall
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA01003
| | - Botond Tyukodi
- Department of Physics, Babes-Bolyai University, Cluj-Napoca400084, Romania
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA02453
| | - Michael F. Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA02453
| | - Christian D. Santangelo
- Department of Physics, University of Massachusetts, Amherst, MA01003
- Department of Physics, Syracuse University, Syracuse, NY13210
| | - Gregory M. Grason
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA01003
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2
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Chandrasekaran A, Graham K, Stachowiak JC, Rangamani P. Kinetic trapping organizes actin filaments within liquid-like protein droplets. Nat Commun 2024; 15:3139. [PMID: 38605007 PMCID: PMC11009352 DOI: 10.1038/s41467-024-46726-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Accepted: 03/07/2024] [Indexed: 04/13/2024] Open
Abstract
Several actin-binding proteins (ABPs) phase separate to form condensates capable of curating the actin network shapes. Here, we use computational modeling to understand the principles of actin network organization within VASP condensate droplets. Our simulations reveal that the different actin shapes, namely shells, rings, and mixture states are highly dependent on the kinetics of VASP-actin interactions, suggesting that they arise from kinetic trapping. Specifically, we show that reducing the residence time of VASP on actin filaments reduces degree of bundling, thereby promoting assembly of shells rather than rings. We validate the model predictions experimentally using a VASP-mutant with decreased bundling capability. Finally, we investigate the ring opening within deformed droplets and found that the sphere-to-ellipsoid transition is favored under a wide range of filament lengths while the ellipsoid-to-rod transition is only permitted when filaments have a specific range of lengths. Our findings highlight key mechanisms of actin organization within phase-separated ABPs.
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Affiliation(s)
- Aravind Chandrasekaran
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA, 92093-0411, USA
| | - Kristin Graham
- Department of Biomedical Engineering, University of Texas at Austin, Austin, TX, 78712, USA
| | - Jeanne C Stachowiak
- Department of Biomedical Engineering, University of Texas at Austin, Austin, TX, 78712, USA.
- Department of Chemical Engineering, University of Texas at Austin, Austin, TX, 78712, USA.
| | - Padmini Rangamani
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA, 92093-0411, USA.
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3
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Yellam K, Priyadarshi A, Jha PK. Monte Carlo simulations of spherocylinders interacting with site-dependent square-well potentials. Sci Rep 2024; 14:3753. [PMID: 38355955 PMCID: PMC10866863 DOI: 10.1038/s41598-024-53182-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2023] [Accepted: 01/29/2024] [Indexed: 02/16/2024] Open
Abstract
Monte Carlo simulations are performed to study the self-assembly of a dilute system of spherocylinders interacting with square-well potential. The interactions are defined between randomly placed sites on the axis of the spherocylinder, akin to the interacting groups on a rigid rodlike molecule. This model therefore also serves as a minimal coarse-grained representation of a system of low molecular weight or stiff polymers with contour lengths significantly lower than the persistence length, interacting predominantly with short-range interactions (e.g., hydrogen bonding). The spherocylinder concentration, square-well interaction strength and range, and fraction of interacting sites are varied to study the phase behavior of the system. We observe the formation of dispersed, bundled, and network configurations of the system that may be compared with previous atomistic simulation results of weak polyelectrolytes.
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Affiliation(s)
- Kiranmai Yellam
- Department of Chemical Engineering, IIT Roorkee, Roorkee, Uttarakhand, 247667, India
| | - Anshuman Priyadarshi
- Department of Chemical Engineering, IIT Roorkee, Roorkee, Uttarakhand, 247667, India
| | - Prateek K Jha
- Department of Chemical Engineering, IIT Roorkee, Roorkee, Uttarakhand, 247667, India.
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4
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Wei WS, Trubiano A, Sigl C, Paquay S, Dietz H, Hagan MF, Fraden S. Hierarchical assembly is more robust than egalitarian assembly in synthetic capsids. Proc Natl Acad Sci U S A 2024; 121:e2312775121. [PMID: 38324570 PMCID: PMC10873614 DOI: 10.1073/pnas.2312775121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Accepted: 12/07/2023] [Indexed: 02/09/2024] Open
Abstract
Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and concentrations of subunits. By contrast, we introduce an assembly paradigm that allows large error-tolerance in the subunit affinity and helps avoid kinetic traps. Our combined experimental and computational approach uses a model system of triangular subunits programmed to assemble into T = 3 icosahedral capsids comprising 60 units. The experimental platform uses DNA origami to create monodisperse colloids whose three-dimensional geometry is controlled to nanometer precision, with two distinct bonds whose affinities are controlled to kBT precision, quantified in situ by static light scattering. The computational model uses a coarse-grained representation of subunits, short-ranged potentials, and Langevin dynamics. Experimental observations and modeling reveal that when the bond affinities are unequal, two distinct hierarchical assembly pathways occur, in which the subunits first form dimers in one case and pentamers in another. These hierarchical pathways produce complete capsids faster and are more robust against affinity variation than egalitarian pathways, in which all binding sites have equal strengths. This finding suggests that hierarchical assembly may be a general engineering principle for optimizing self-assembly of complex target structures.
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Affiliation(s)
- Wei-Shao Wei
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA02453
- Materials Research Science and Engineering Center, Brandeis University, Waltham, MA02453
| | - Anthony Trubiano
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA02453
- Materials Research Science and Engineering Center, Brandeis University, Waltham, MA02453
| | - Christian Sigl
- Laboratory for Biomolecular Nanotechnology, Department of Physics, Technical University of Munich, Garching85748, Germany
- Munich Institute of Biomedical Engineering, Technical University of Munich, Garching85748, Germany
| | - Stefan Paquay
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA02453
- Materials Research Science and Engineering Center, Brandeis University, Waltham, MA02453
| | - Hendrik Dietz
- Laboratory for Biomolecular Nanotechnology, Department of Physics, Technical University of Munich, Garching85748, Germany
- Munich Institute of Biomedical Engineering, Technical University of Munich, Garching85748, Germany
| | - Michael F. Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA02453
- Materials Research Science and Engineering Center, Brandeis University, Waltham, MA02453
| | - Seth Fraden
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA02453
- Materials Research Science and Engineering Center, Brandeis University, Waltham, MA02453
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5
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Lang L, Böhler H, Wagler H, Beck T. Assembly Requirements for the Construction of Large-Scale Binary Protein Structures. Biomacromolecules 2024; 25:177-187. [PMID: 38059469 DOI: 10.1021/acs.biomac.3c00891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/08/2023]
Abstract
The precise assembly of multiple biomacromolecules into well-defined structures and materials is of great importance for various biomedical and nanobiotechnological applications. In this study, we investigate the assembly requirements for two-component materials using charged protein nanocages as building blocks. To achieve this, we designed several variants of ferritin nanocages to determine the surface characteristics necessary for the formation of large-scale binary three-dimensional (3D) assemblies. These nanocage variants were employed in protein crystallization experiments and macromolecular crystallography analyses, complemented by computational methods. Through the screening of nanocage variant combinations at various ionic strengths, we identified three essential features for successful assembly: (1) the presence of a favored crystal contact region, (2) the presence of a charged patch not involved in crystal contacts, and (3) sufficient distinctiveness between the nanocages. Surprisingly, the absence of noncrystal contact mediating patches had a detrimental effect on the assemblies, highlighting their unexpected importance. Intriguingly, we observed the formation of not only binary structures but also both negatively and positively charged unitary structures under previously exclusively binary conditions. Overall, our findings will inform future design strategies by providing some design rules, showcasing the utility of supercharging symmetric building blocks in facilitating the assembly of biomacromolecules into large-scale binary 3D assemblies.
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Affiliation(s)
- Laurin Lang
- Institute of Physical Chemistry, Department of Chemistry, Universität Hamburg, Grindelallee 117, 20146 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Hendrik Böhler
- Institute of Physical Chemistry, Department of Chemistry, Universität Hamburg, Grindelallee 117, 20146 Hamburg, Germany
| | - Henrike Wagler
- Institute of Physical Chemistry, Department of Chemistry, Universität Hamburg, Grindelallee 117, 20146 Hamburg, Germany
| | - Tobias Beck
- Institute of Physical Chemistry, Department of Chemistry, Universität Hamburg, Grindelallee 117, 20146 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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6
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Tiwari AK, Sen D, Das A, Bahadur J. Evidence of Size Stratification in Colloidal Glass Microgranules Realized by Rapid Evaporative Assembly. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:15572-15586. [PMID: 37882047 DOI: 10.1021/acs.langmuir.3c01872] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2023]
Abstract
Evaporation is a ubiquitous phenomenon. Rapid evaporation of the continuous phase from micrometric colloidal droplets can be used to realize nanostructured microgranules, constituting the assembled nanoparticles. One of the important aspects of such nonequilibrium assembly is the nature of the packing of nanoparticles in the microgranules. The present work demonstrates the evidence of size stratification of the nanoparticles in such far-from-equilibrium configurations. Small-angle X-ray scattering, in combination with particle packing simulation, reveals the "large on top"-type stratification in such assembled microgranules, where the larger particles get concentrated at the outer shell of the granules while the smaller particles reside in the core region. It also reveals the presence of local clusters in such a rapid evaporative assembly in aerosolized colloidal droplets.
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Affiliation(s)
- Anand Kumar Tiwari
- Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
- Homi Bhabha National Institute, Anushaktinagar, Mumbai 400 094, India
| | - Debasis Sen
- Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
- Homi Bhabha National Institute, Anushaktinagar, Mumbai 400 094, India
| | - Avik Das
- Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
| | - Jitendra Bahadur
- Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
- Homi Bhabha National Institute, Anushaktinagar, Mumbai 400 094, India
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7
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Asor R, Singaram SW, Levi-Kalisman Y, Hagan MF, Raviv U. Effect of ionic strength on the assembly of simian vacuolating virus capsid protein around poly(styrene sulfonate). THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:107. [PMID: 37917241 DOI: 10.1140/epje/s10189-023-00363-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 10/09/2023] [Indexed: 11/04/2023]
Abstract
Virus-like particles (VLPs) are noninfectious nanocapsules that can be used for drug delivery or vaccine applications. VLPs can be assembled from virus capsid proteins around a condensing agent, such as RNA, DNA, or a charged polymer. Electrostatic interactions play an important role in the assembly reaction. VLPs assemble from many copies of capsid protein, with a combinatorial number of intermediates. Hence, the mechanism of the reaction is poorly understood. In this paper, we combined solution small-angle X-ray scattering (SAXS), cryo-transmission electron microscopy (TEM), and computational modeling to determine the effect of ionic strength on the assembly of Simian Vacuolating Virus 40 (SV40)-like particles. We mixed poly(styrene sulfonate) with SV40 capsid protein pentamers at different ionic strengths. We then characterized the assembly product by SAXS and cryo-TEM. To analyze the data, we performed Langevin dynamics simulations using a coarse-grained model that revealed incomplete, asymmetric VLP structures consistent with the experimental data. We found that close to physiological ionic strength, [Formula: see text] VLPs coexisted with VP1 pentamers. At lower or higher ionic strengths, incomplete particles coexisted with pentamers and [Formula: see text] particles. Including the simulated structures was essential to explain the SAXS data in a manner that is consistent with the cryo-TEM images.
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Affiliation(s)
- Roi Asor
- Institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, 9190401, Jerusalem, Israel
| | - Surendra W Singaram
- Department of Physics, Brandeis University, 415 South Street, Waltham, 02453, MA, USA
| | - Yael Levi-Kalisman
- Institute of Life Sciences and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, 9190401, Jerusalem, Israel
| | - Michael F Hagan
- Department of Physics, Brandeis University, 415 South Street, Waltham, 02453, MA, USA.
| | - Uri Raviv
- Institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, 9190401, Jerusalem, Israel.
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8
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Hagan MF, Mohajerani F. Self-assembly coupled to liquid-liquid phase separation. PLoS Comput Biol 2023; 19:e1010652. [PMID: 37186597 PMCID: PMC10212142 DOI: 10.1371/journal.pcbi.1010652] [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: 10/12/2022] [Revised: 05/25/2023] [Accepted: 04/26/2023] [Indexed: 05/17/2023] Open
Abstract
Liquid condensate droplets with distinct compositions of proteins and nucleic acids are widespread in biological cells. While it is known that such droplets, or compartments, can regulate irreversible protein aggregation, their effect on reversible self-assembly remains largely unexplored. In this article, we use kinetic theory and solution thermodynamics to investigate the effect of liquid-liquid phase separation on the reversible self-assembly of structures with well-defined sizes and architectures. We find that, when assembling subunits preferentially partition into liquid compartments, robustness against kinetic traps and maximum achievable assembly rates can be significantly increased. In particular, both the range of solution conditions leading to productive assembly and the corresponding assembly rates can increase by orders of magnitude. We analyze the rate equation predictions using simple scaling estimates to identify effects of liquid-liquid phase separation as a function of relevant control parameters. These results may elucidate self-assembly processes that underlie normal cellular functions or pathogenesis, and suggest strategies for designing efficient bottom-up assembly for nanomaterials applications.
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Affiliation(s)
- Michael F. Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts, United States of America
| | - Farzaneh Mohajerani
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts, United States of America
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9
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Picard JAKL, Speck T. Inverse condensation of adsorbed molecules with two conformations. J Chem Phys 2023; 158:034701. [PMID: 36681634 DOI: 10.1063/5.0133965] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
Conventional gas-liquid phase transitions feature a coexistence line that has a monotonic and positive slope in line with our intuition that cooling always leads to condensation. Here, we study the inverse phenomenon, condensation of adsorbed organic molecules into dense domains upon heating. Our considerations are motivated by recent experiments [Aeschlimann et al., Angew. Chem., Int. Ed. 60, 19117-19122 (2021)], which demonstrate the partial dissolution of an ordered molecular monolayer and the mobilization of molecules upon cooling. We introduce a simple lattice model in which each site can have three states corresponding to unoccupied and two discernible molecular conformations. We investigate this model through Monte Carlo simulations, mean-field theory, and exact results based on the analytical solution of the Ising model in two dimensions. Our results should be broadly applicable to molecules with distinct conformations that have sufficiently different entropies or heat capacities.
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Affiliation(s)
- Joël A K L Picard
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Thomas Speck
- Institute for Theoretical Physics IV, University of Stuttgart, 70569 Stuttgart, Germany
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10
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Dwivedi M, Singh SL, Bharadwaj AS, Kishore V, Singh AV. Self-Assembly of DNA-Grafted Colloids: A Review of Challenges. MICROMACHINES 2022; 13:mi13071102. [PMID: 35888919 PMCID: PMC9324607 DOI: 10.3390/mi13071102] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/11/2022] [Revised: 07/05/2022] [Accepted: 07/12/2022] [Indexed: 02/04/2023]
Abstract
DNA-mediated self-assembly of colloids has emerged as a powerful tool to assemble the materials of prescribed structure and properties. The uniqueness of the approach lies in the sequence-specific, thermo-reversible hybridization of the DNA-strands based on Watson–Crick base pairing. Grafting particles with DNA strands, thus, results into building blocks that are fully programmable, and can, in principle, be assembled into any desired structure. There are, however, impediments that hinder the DNA-grafted particles from realizing their full potential, as building blocks, for programmable self-assembly. In this short review, we focus on these challenges and highlight the research around tackling these challenges.
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Affiliation(s)
- Manish Dwivedi
- Department of Physics, Banaras Hindu University, Varanasi 221005, UP, India; (M.D.); (V.K.)
| | - Swarn Lata Singh
- Department of Physics, Mahila Mahavidyalaya (MMV), Banaras Hindu University, Varanasi 221005, UP, India
- Correspondence: (S.L.S.); (A.V.S.)
| | - Atul S. Bharadwaj
- Department of Physics, CMP Degree College, University of Allahabad, Prayagraj 211002, UP, India;
| | - Vimal Kishore
- Department of Physics, Banaras Hindu University, Varanasi 221005, UP, India; (M.D.); (V.K.)
| | - Ajay Vikram Singh
- Department of Chemical and Product Safety, German Federal Institute of Risk Assessment (BfR), Maxdohrnstrasse 8-10, 10589 Berlin, Germany
- Correspondence: (S.L.S.); (A.V.S.)
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11
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Indelicato G, Cermelli P, Twarock R. Local rules for the self-assembly of a non-quasi-equivalent viral capsid. Phys Rev E 2022; 105:064403. [PMID: 35854534 DOI: 10.1103/physreve.105.064403] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 05/05/2022] [Indexed: 06/15/2023]
Abstract
The structures of many large bacteriophages, such as the P23-77 capsids, do not adhere strictly to the quasi-equivalence principle of viral architecture. Although the general architecture of the P23-77 capsids is classed as T=28d, it self-assembles from multiple copies of two types of coat protein subunits, and the resulting hexameric capsomers do not conform to the Caspar-Klug paradigm. There are two types of hexamers with distinct internal organization, that are located at specific positions in the capsid. It is an open problem which assembly mechanism can lead to such a complex capsid organization. Here we propose a simple set of local rules that can explain how such non-quasi-equivalent capsid structures can arise as a result of self-assembly.
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Affiliation(s)
| | - Paolo Cermelli
- Dipartimento di Matematica, Università di Torino, 10123 Torino TO, Italy
| | - Reidun Twarock
- Department of Mathematics and Department of Biology, University of York, York, YO10 5DD, United Kingdom
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12
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Mizrahi I, Bruinsma R, Rudnick J. Packaging contests between viral RNA molecules and kinetic selectivity. PLoS Comput Biol 2022; 18:e1009913. [PMID: 35363785 PMCID: PMC9022832 DOI: 10.1371/journal.pcbi.1009913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2021] [Revised: 04/21/2022] [Accepted: 02/09/2022] [Indexed: 11/18/2022] Open
Abstract
The paper presents a statistical-mechanics model for the kinetic selection of viral RNA molecules by packaging signals during the nucleation stage of the assembly of small RNA viruses. The effects of the RNA secondary structure and folding geometry of the packaging signals on the assembly activation energy barrier are encoded by a pair of characteristics: the wrapping number and the maximum ladder distance. Kinetic selection is found to be optimal when assembly takes place under conditions of supersaturation and also when the concentration ratio of capsid protein and viral RNA concentrations equals the stoichiometric ratio of assembled viral particles. As a function of the height of the activation energy barrier, there is a form of order-disorder transition such that for sufficiently low activation energy barriers, kinetic selectivity is erased by entropic effects associated with the number of assembly pathways.
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Affiliation(s)
- Inbal Mizrahi
- Department of Physics and Astronomy, University of California, Los Angeles, California, United States of America
| | - Robijn Bruinsma
- Department of Physics and Astronomy, University of California, Los Angeles, California, United States of America
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California, United States of America
- * E-mail:
| | - Joseph Rudnick
- Department of Physics and Astronomy, University of California, Los Angeles, California, United States of America
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13
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Guo SK, Sodt AJ, Johnson ME. Large self-assembled clathrin lattices spontaneously disassemble without sufficient adaptor proteins. PLoS Comput Biol 2022; 18:e1009969. [PMID: 35312692 PMCID: PMC8979592 DOI: 10.1371/journal.pcbi.1009969] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2021] [Revised: 03/31/2022] [Accepted: 02/24/2022] [Indexed: 11/18/2022] Open
Abstract
Clathrin-coated structures must assemble on cell membranes to internalize receptors, with the clathrin protein only linked to the membrane via adaptor proteins. These structures can grow surprisingly large, containing over 20 clathrin, yet they often fail to form productive vesicles, instead aborting and disassembling. We show that clathrin structures of this size can both form and disassemble spontaneously when adaptor protein availability is low, despite high abundance of clathrin. Here, we combine recent in vitro kinetic measurements with microscopic reaction-diffusion simulations and theory to differentiate mechanisms of stable vs unstable clathrin assembly on membranes. While in vitro conditions drive assembly of robust, stable lattices, we show that concentrations, geometry, and dimensional reduction in physiologic-like conditions do not support nucleation if only the key adaptor AP-2 is included, due to its insufficient abundance. Nucleation requires a stoichiometry of adaptor to clathrin that exceeds 1:1, meaning additional adaptor types are necessary to form lattices successfully and efficiently. We show that the critical nucleus contains ~25 clathrin, remarkably similar to sizes of the transient and abortive structures observed in vivo. Lastly, we quantify the cost of bending the membrane under our curved clathrin lattices using a continuum membrane model. We find that the cost of bending the membrane could be largely offset by the energetic benefit of forming curved rather than flat structures, with numbers comparable to experiments. Our model predicts how adaptor density can tune clathrin-coated structures from the transient to the stable, showing that active energy consumption is therefore not required for lattice disassembly or remodeling during growth, which is a critical advance towards predicting productive vesicle formation.
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Affiliation(s)
- Si-Kao Guo
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland, United States of America
| | - Alexander J. Sodt
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland, United States of America
| | - Margaret E. Johnson
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland, United States of America
- * E-mail:
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14
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Harmon TS, Jülicher F. Molecular Assembly Lines in Active Droplets. PHYSICAL REVIEW LETTERS 2022; 128:108102. [PMID: 35333067 DOI: 10.1103/physrevlett.128.108102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Revised: 11/30/2021] [Accepted: 01/21/2022] [Indexed: 06/14/2023]
Abstract
Large protein complexes are assembled from protein subunits to form a specific structure. In our theoretic work, we propose that assembly into the correct structure could be reliably achieved through an assembly line with a specific sequence of assembly steps. Using droplet interfaces to position compartment boundaries, we show that an assembly line can be self-organized by active droplets. As a consequence, assembly steps can be arranged spatially so that a specific order of assembly is achieved and incorrect assembly is strongly suppressed.
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Affiliation(s)
- Tyler S Harmon
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzerstraße 38, 01187 Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany
- Leibniz-Institut für Polymerforschung Dresden e.V., Hohestraße 6, 01069 Dresden, Germany
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzerstraße 38, 01187 Dresden, Germany
- Center for Systems Biology Dresden, 01307 Dresden, Germany
- Cluster of Excellence Physics of Life, TU Dresden, 01062 Dresden, Germany
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15
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Abstract
Time efficiency of self-assembly is crucial for many biological processes. Moreover, with the advances of nanotechnology, time efficiency in artificial self-assembly becomes ever more important. While structural determinants and the final assembly yield are increasingly well understood, kinetic aspects concerning the time efficiency, however, remain much more elusive. In computer science, the concept of time complexity is used to characterize the efficiency of an algorithm and describes how the algorithm's runtime depends on the size of the input data. Here we characterize the time complexity of nonequilibrium self-assembly processes by exploring how the time required to realize a certain, substantial yield of a given target structure scales with its size. We identify distinct classes of assembly scenarios, i.e., "algorithms" to accomplish this task, and show that they exhibit drastically different degrees of complexity. Our analysis enables us to identify optimal control strategies for nonequilibrium self-assembly processes. Furthermore, we suggest an efficient irreversible scheme for the artificial self-assembly of nanostructures, which complements the state-of-the-art approach using reversible binding reactions and requires no fine-tuning of binding energies.
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16
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Safaei S, Todd C, Yarndley J, Hendy S, Willmott GR. Asymmetric assembly of Lennard-Jones Janus dimers. Phys Rev E 2021; 104:024602. [PMID: 34525533 DOI: 10.1103/physreve.104.024602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Accepted: 07/22/2021] [Indexed: 11/07/2022]
Abstract
Self-assembly of Janus (or "patchy") particles is dependent on the precise interaction between neighboring particles. Here, the orientations of two amphiphilic Janus spheres within a dimer in an explicit fluid are studied with high geometric resolution. Molecular dynamics simulations and semianalytical energy calculations are used with hard- and soft-sphere Lennard-Jones potentials, and temperature and hydrophobicity are varied. The most probable center-center-pole angles are in the range of 40^{∘}-55^{∘} with pole-to-pole alignment not observed due to orientational entropy. Angles near 90^{∘} are energetically unfavored due to solvent exclusion, and the relative azimuthal angle between the spheres is affected by solvent ordering. Relatively large polar angles become more favored as the hydrophobic surface area (i.e., Janus balance) is increased.
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Affiliation(s)
- Sina Safaei
- The MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, Wellington 6140, New Zealand.,Department of Physics, University of Auckland, Auckland 1010, New Zealand
| | - Caleb Todd
- Department of Physics, University of Auckland, Auckland 1010, New Zealand
| | - Jack Yarndley
- Department of Physics, University of Auckland, Auckland 1010, New Zealand
| | - Shaun Hendy
- The MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, Wellington 6140, New Zealand.,Department of Physics, University of Auckland, Auckland 1010, New Zealand.,Te Pūnaha Matatini, University of Auckland, Auckland 1010, New Zealand
| | - Geoff R Willmott
- The MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, Wellington 6140, New Zealand.,Department of Physics, University of Auckland, Auckland 1010, New Zealand.,School of Chemical Sciences, University of Auckland, Auckland 1010, New Zealand
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17
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Mishra B, Johnson ME. Speed limits of protein assembly with reversible membrane localization. J Chem Phys 2021; 154:194101. [PMID: 34240891 PMCID: PMC8131109 DOI: 10.1063/5.0045867] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 04/26/2021] [Indexed: 12/15/2022] Open
Abstract
Protein assembly is often studied in a three-dimensional solution, but a significant fraction of binding events involve proteins that can reversibly bind and diffuse along a two-dimensional surface. In a recent study, we quantified how proteins can exploit the reduced dimensionality of the membrane to trigger complex formation. Here, we derive a single expression for the characteristic timescale of this multi-step assembly process, where the change in dimensionality renders rates and concentrations effectively time-dependent. We find that proteins can accelerate dimer formation due to an increase in relative concentration, driving more frequent collisions, which often win out over slow-downs due to diffusion. Our model contains two protein populations that dimerize with one another and use a distinct site to bind membrane lipids, creating a complex reaction network. However, by identifying two major rate-limiting pathways to reach an equilibrium steady-state, we derive an excellent approximation for the mean first passage time when lipids are in abundant supply. Our theory highlights how the "sticking rate" or effective adsorption coefficient of the membrane is central in controlling timescales. We also derive a corrected localization rate to quantify how the geometry of the system and diffusion can reduce rates of membrane localization. We validate and test our results using kinetic and particle-based reaction-diffusion simulations. Our results establish how the speed of key assembly steps can shift by orders-of-magnitude when membrane localization is possible, which is critical to understanding mechanisms used in cells.
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Affiliation(s)
- Bhavya Mishra
- TC Jenkins Department of Biophysics, Johns Hopkins University, 3400 N Charles St., Baltimore, Maryland 21218, USA
| | - Margaret E. Johnson
- TC Jenkins Department of Biophysics, Johns Hopkins University, 3400 N Charles St., Baltimore, Maryland 21218, USA
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18
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Immature HIV-1 assembles from Gag dimers leaving partial hexamers at lattice edges as potential substrates for proteolytic maturation. Proc Natl Acad Sci U S A 2021; 118:2020054118. [PMID: 33397805 PMCID: PMC7826355 DOI: 10.1073/pnas.2020054118] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
HIV-1 particle assembly is driven by the viral Gag protein, which oligomerizes into a hexameric array on the inner surface of the viral envelope, forming a truncated spherical lattice containing large and small gaps. Gag is then cut by the viral protease, disassembles, and rearranges to form the mature, infectious virus. Here, we present structures and molecular dynamics simulations of the edges of the immature Gag lattice. Our analysis shows that Gag dimers are the basic assembly unit of the HIV-1 particle, lattice edges are partial hexamers, and partial hexamers are prone to structural changes allowing protease to cut Gag. These findings provide insights into assembly of the immature virus, its structure, and how it disassembles during maturation. The CA (capsid) domain of immature HIV-1 Gag and the adjacent spacer peptide 1 (SP1) play a key role in viral assembly by forming a lattice of CA hexamers, which adapts to viral envelope curvature by incorporating small lattice defects and a large gap at the site of budding. This lattice is stabilized by intrahexameric and interhexameric CA-CA interactions, which are important in regulating viral assembly and maturation. We applied subtomogram averaging and classification to determine the oligomerization state of CA at lattice edges and found that CA forms partial hexamers. These structures reveal the network of interactions formed by CA-SP1 at the lattice edge. We also performed atomistic molecular dynamics simulations of CA-CA interactions stabilizing the immature lattice and partial CA-SP1 helical bundles. Free energy calculations reveal increased propensity for helix-to-coil transitions in partial hexamers compared to complete six-helix bundles. Taken together, these results suggest that the CA dimer is the basic unit of lattice assembly, partial hexamers exist at lattice edges, these are in a helix-coil dynamic equilibrium, and partial helical bundles are more likely to unfold, representing potential sites for HIV-1 maturation initiation.
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19
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Hagan MF, Grason GM. Equilibrium mechanisms of self-limiting assembly. REVIEWS OF MODERN PHYSICS 2021; 93:025008. [PMID: 35221384 PMCID: PMC8880259 DOI: 10.1103/revmodphys.93.025008] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits "measure" and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter - micellization of amphiphiles and shell/tubule formation of tapered subunits - as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.
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Affiliation(s)
- Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02454, USA
| | - Gregory M Grason
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003, USA
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20
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Mohajerani F, Sayer E, Neil C, Inlow K, Hagan MF. Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control. ACS NANO 2021; 15:4197-4212. [PMID: 33683101 PMCID: PMC8058603 DOI: 10.1021/acsnano.0c05715] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
This article describes a theoretical and computational study of the dynamical assembly of a protein shell around a complex consisting of many cargo molecules and long, flexible scaffold molecules. Our study is motivated by bacterial microcompartments, which are proteinaceous organelles that assemble around a condensed droplet of enzymes and reactants. As in many examples of cytoplasmic liquid-liquid phase separation, condensation of the microcompartment interior cargo is driven by flexible scaffold proteins that have weak multivalent interactions with the cargo. Our results predict that the shell size, amount of encapsulated cargo, and assembly pathways depend sensitively on properties of the scaffold, including its length and valency of scaffold-cargo interactions. Moreover, the ability of self-assembling protein shells to change their size to accommodate scaffold molecules of different lengths depends crucially on whether the spontaneous curvature radius of the protein shell is smaller or larger than a characteristic elastic length scale of the shell. Beyond natural microcompartments, these results have important implications for synthetic biology efforts to target alternative molecules for encapsulation by microcompartments or viral shells. More broadly, the results elucidate how cells exploit coupling between self-assembly and liquid-liquid phase separation to organize their interiors.
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Affiliation(s)
- Farzaneh Mohajerani
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Evan Sayer
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Christopher Neil
- Department of Biochemistry, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Koe Inlow
- Department of Biochemistry, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Michael F Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
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21
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Zhang TD, Chen LL, Lin WJ, Shi WP, Wang JQ, Zhang CY, Guo WH, Deng X, Yin DC. Searching for conditions of protein self-assembly by protein crystallization screening method. Appl Microbiol Biotechnol 2021; 105:2759-2773. [PMID: 33683398 DOI: 10.1007/s00253-021-11188-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2020] [Revised: 01/29/2021] [Accepted: 02/17/2021] [Indexed: 11/28/2022]
Abstract
The self-assembly of biomacromolecules is an extremely important process. It is potentially useful in the fields of life science and materials science. To carry out the study on the self-assembly of proteins, it is necessary to find out the suitable self-assembly conditions, which have always been a challenging task in practice. Inspired by the screening technique in the field of protein crystallization, we proposed using the same screening technique for seeking suitable protein self-assembly conditions. Based on this consideration, we selected 5 proteins (β-lactoglobulin, hemoglobin, pepsin, lysozyme, α-chymotrypsinogen (II) A) together with 5 screening kits (IndexTM, BML, Morpheus, JCSG, PEG/Ion ScreenTM) to investigate the performance of these crystallization screening techniques in order to discover new optimized conditions of protein self-assembly. The screens were all kept at 293 K for certain days, and were analyzed using optical microscope, scanning electron microscope, transmission electron microscope, atomic force microscope, fluorescence microscope, and atomic absorption spectroscope. The results demonstrated that the method of protein crystallization screening can be successfully applied in the screening of self-assembly conditions. This method is fast, high throughput, and easily implemented in an automated system, with a low protein consumption feature. These results suggested that such strategy can be applied to finding new conditions or forms in routine research of protein self-assembly. KEY POINTS: • Protein crystallization screening method is successfully applied in the screening of self-assembly conditions. • This screening method can be applied on various kinds of proteins and possess a feature of low protein consumption. • This screening method is fast, high throughput, and easily implemented in an automated system.
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Affiliation(s)
- Tuo-Di Zhang
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, China
| | - Liang-Liang Chen
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, China
| | - Wen-Juan Lin
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, China
| | - Wen-Pu Shi
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, China
| | - Jia-Qi Wang
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, China
| | - Chen-Yan Zhang
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, China
| | | | - Xudong Deng
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, China.
| | - Da-Chuan Yin
- Key Laboratory for Space Bioscience and Biotechnology, School of Life Sciences, Northwestern Polytechnical University, Xi'an, 710072, China.
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22
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Bruinsma RF, Wuite GJL, Roos WH. Physics of viral dynamics. NATURE REVIEWS. PHYSICS 2021; 3:76-91. [PMID: 33728406 PMCID: PMC7802615 DOI: 10.1038/s42254-020-00267-1] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/20/2020] [Indexed: 05/12/2023]
Abstract
Viral capsids are often regarded as inert structural units, but in actuality they display fascinating dynamics during different stages of their life cycle. With the advent of single-particle approaches and high-resolution techniques, it is now possible to scrutinize viral dynamics during and after their assembly and during the subsequent development pathway into infectious viruses. In this Review, the focus is on the dynamical properties of viruses, the different physical virology techniques that are being used to study them, and the physical concepts that have been developed to describe viral dynamics.
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Affiliation(s)
- Robijn F. Bruinsma
- Department of Physics and Astronomy, University of California, Los Angeles, California, USA
| | - Gijs J. L. Wuite
- Fysica van levende systemen, Vrije Universiteit, Amsterdam, the Netherlands
| | - Wouter H. Roos
- Moleculaire Biofysica, Zernike Instituut, Rijksuniversiteit Groningen, Groningen, the Netherlands
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23
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Schlicksup CJ, Zlotnick A. Viral structural proteins as targets for antivirals. Curr Opin Virol 2020; 45:43-50. [PMID: 32777753 DOI: 10.1016/j.coviro.2020.07.001] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2020] [Revised: 06/30/2020] [Accepted: 07/01/2020] [Indexed: 12/29/2022]
Abstract
Viral structural proteins are emerging as effective targets for new antivirals. In a viral lifecycle, the capsid must assemble, disassemble, and respond to host proteins, all at the right time and place. These reactions work within a narrow range of conditions, making them susceptible to small molecule interference. In at least three specific viruses, this approach has had met with preliminary success. In rhinovirus and poliovirus, compounds like pleconaril bind capsid and block RNA release. Bevirimat binds to Gag protein in HIV, inhibiting maturation. In Hepatitis B virus, core protein allosteric modulators (CpAMs) promote spontaneous assembly of capsid protein leading to empty and aberrant particles. Despite the biological diversity between viruses and the chemical diversity between antiviral molecules, we observe common features in these antivirals' mechanisms of action. These approaches work by stabilizing protein-protein interactions.
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Affiliation(s)
- Christopher John Schlicksup
- Molecular and Cellular Biology Department, Indiana University-Bloomington, Bloomington, IN 47401, United States
| | - Adam Zlotnick
- Molecular and Cellular Biology Department, Indiana University-Bloomington, Bloomington, IN 47401, United States.
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24
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Schlicksup CJ, Laughlin P, Dunkelbarger S, Wang JCY, Zlotnick A. Local Stabilization of Subunit-Subunit Contacts Causes Global Destabilization of Hepatitis B Virus Capsids. ACS Chem Biol 2020; 15:1708-1717. [PMID: 32369333 DOI: 10.1021/acschembio.0c00320] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Development of antiviral molecules that bind virion is a strategy that remains in its infancy, and the details of their mechanisms are poorly understood. Here we investigate the behavior of DBT1, a dibenzothiazepine that specifically interacts with the capsid protein of hepatitis B virus (HBV). We found that DBT1 stabilizes protein-protein interaction, accelerates capsid assembly, and can induce formation of aberrant particles. Paradoxically, DBT1 can cause preformed capsids to dissociate. These activities may lead to (i) assembly of empty and defective capsids, inhibiting formation of new virus, and (ii) disruption of mature viruses, which are metastable, to inhibit new infection. Using cryo-electron microscopy, we observed that DBT1 led to asymmetric capsids where well-defined DBT1 density was bound at all intersubunit contacts. These results suggest that DBT1 can support assembly by increasing buried surface area but induce disassembly of metastable capsids by favoring asymmetry to induce structural defects.
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Affiliation(s)
- Christopher John Schlicksup
- Molecular and Cellular Biology Department, Indiana University—Bloomington, Bloomington, Indiana 47401, United States
| | - Patrick Laughlin
- Molecular and Cellular Biology Department, Indiana University—Bloomington, Bloomington, Indiana 47401, United States
| | - Steven Dunkelbarger
- Molecular and Cellular Biology Department, Indiana University—Bloomington, Bloomington, Indiana 47401, United States
| | - Joseph Che-Yen Wang
- Molecular and Cellular Biology Department, Indiana University—Bloomington, Bloomington, Indiana 47401, United States
- Department of Microbiology and Immunology, Pennsylvania State University College of Medicine, Hershey, Pennsylvania 17033, United States
| | - Adam Zlotnick
- Molecular and Cellular Biology Department, Indiana University—Bloomington, Bloomington, Indiana 47401, United States
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25
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Varga MJ, Fu Y, Loggia S, Yogurtcu ON, Johnson ME. NERDSS: A Nonequilibrium Simulator for Multibody Self-Assembly at the Cellular Scale. Biophys J 2020; 118:3026-3040. [PMID: 32470324 DOI: 10.1016/j.bpj.2020.05.002] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2019] [Revised: 04/24/2020] [Accepted: 05/05/2020] [Indexed: 12/13/2022] Open
Abstract
Currently, a significant barrier to building predictive models of cellular self-assembly processes is that molecular models cannot capture minutes-long dynamics that couple distinct components with active processes, whereas reaction-diffusion models cannot capture structures of molecular assembly. Here, we introduce the nonequilibrium reaction-diffusion self-assembly simulator (NERDSS), which addresses this spatiotemporal resolution gap. NERDSS integrates efficient reaction-diffusion algorithms into generalized software that operates on user-defined molecules through diffusion, binding and orientation, unbinding, chemical transformations, and spatial localization. By connecting the fast processes of binding with the slow timescales of large-scale assembly, NERDSS integrates molecular resolution with reversible formation of ordered, multisubunit complexes. NERDSS encodes models using rule-based formatting languages to facilitate model portability, usability, and reproducibility. Applying NERDSS to steps in clathrin-mediated endocytosis, we design multicomponent systems that can form lattices in solution or on the membrane, and we predict how stochastic but localized dephosphorylation of membrane lipids can drive lattice disassembly. The NERDSS simulations reveal the spatial constraints on lattice growth and the role of membrane localization and cooperativity in nucleating assembly. By modeling viral lattice assembly and recapitulating oscillations in protein expression levels for a circadian clock model, we illustrate the adaptability of NERDSS. NERDSS simulates user-defined assembly models that were previously inaccessible to existing software tools, with broad applications to predicting self-assembly in vivo and designing high-yield assemblies in vitro.
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Affiliation(s)
- Matthew J Varga
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland
| | - Yiben Fu
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland
| | - Spencer Loggia
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland
| | - Osman N Yogurtcu
- Center for Biologics Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland
| | - Margaret E Johnson
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland.
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26
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Asor R, Schlicksup CJ, Zhao Z, Zlotnick A, Raviv U. Rapidly Forming Early Intermediate Structures Dictate the Pathway of Capsid Assembly. J Am Chem Soc 2020; 142:7868-7882. [PMID: 32233479 PMCID: PMC7242811 DOI: 10.1021/jacs.0c01092] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
There are ∼1030 possible intermediates on the assembly path from hepatitis B capsid protein dimers to the 120-dimer capsid. If every intermediate was tested, assembly would often get stuck in an entropic trap and essentially every capsid would follow a unique assembly path. Yet, capsids assemble rapidly with minimal trapped intermediates, a realization of the Levinthal paradox. To understand the fundamental mechanisms of capsid assembly, it is critical to resolve the early stages of the reaction. We have used time-resolved small angle X-ray scattering, which is sensitive to solute size and shape and has millisecond temporal resolution. Scattering curves were fit to a thermodynamically curated library of assembly intermediates, using the principle of maximum entropy. Maximum entropy also provides a physical rationale for the selection of species. We found that the capsid assembly pathway was exquisitely sensitive to initial assembly conditions. With the mildest conditions tested, the reaction appeared to be two-state from dimer to 120-dimer capsid with some dimers-of-dimers and trimers-of-dimers. In slightly more aggressive conditions, we observed transient accumulation of a decamer-of-dimers and the appearance of 90-dimer capsids. In conditions where there is measurable kinetic trapping, we found that highly diverse early intermediates accumulated within a fraction of a second and propagated into long-lived kinetically trapped states (≥90-mer). In all cases, intermediates between 35 and 90 subunits did not accumulate. These results are consistent with the presence of low barrier paths that connect early and late intermediates and direct the ultimate assembly path to late intermediates where assembly can be paused.
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Affiliation(s)
- Roi Asor
- Institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel
| | - Christopher John Schlicksup
- Molecular and Cellular Biochemistry Department, Indiana University, Bloomington, Indiana 47405, United States
| | - Zhongchao Zhao
- Molecular and Cellular Biochemistry Department, Indiana University, Bloomington, Indiana 47405, United States
| | - Adam Zlotnick
- Molecular and Cellular Biochemistry Department, Indiana University, Bloomington, Indiana 47405, United States
| | - Uri Raviv
- Institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401, Israel
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27
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Sabatino MA, Carfì Pavia F, Rigogliuso S, Giacomazza D, Ghersi G, La Carrubba V, Dispenza C. Development of injectable and durable kefiran hydro-alcoholic gels. Int J Biol Macromol 2020; 149:309-319. [DOI: 10.1016/j.ijbiomac.2020.01.244] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2019] [Revised: 08/25/2019] [Accepted: 01/24/2020] [Indexed: 11/08/2022]
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28
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Gartner FM, Graf IR, Wilke P, Geiger PM, Frey E. Stochastic yield catastrophes and robustness in self-assembly. eLife 2020; 9:51020. [PMID: 32022683 PMCID: PMC7089767 DOI: 10.7554/elife.51020] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Accepted: 02/04/2020] [Indexed: 12/02/2022] Open
Abstract
A guiding principle in self-assembly is that, for high production yield, nucleation of structures must be significantly slower than their growth. However, details of the mechanism that impedes nucleation are broadly considered irrelevant. Here, we analyze self-assembly into finite-sized target structures employing mathematical modeling. We investigate two key scenarios to delay nucleation: (i) by introducing a slow activation step for the assembling constituents and, (ii) by decreasing the dimerization rate. These scenarios have widely different characteristics. While the dimerization scenario exhibits robust behavior, the activation scenario is highly sensitive to demographic fluctuations. These demographic fluctuations ultimately disfavor growth compared to nucleation and can suppress yield completely. The occurrence of this stochastic yield catastrophe does not depend on model details but is generic as soon as number fluctuations between constituents are taken into account. On a broader perspective, our results reveal that stochasticity is an important limiting factor for self-assembly and that the specific implementation of the nucleation process plays a significant role in determining the yield. The self-assembly of a large biological molecule from small building blocks is like finishing a puzzle of magnetic pieces by shaking the box. Even though each piece of the puzzle is attracted to its correct neighbours, the limited control makes it very hard to finish the puzzle in a short amount of time. The problem becomes even more difficult if several copies of the same puzzle are assembled in one box. If several puzzles start at the same time, the different parts might steal pieces from each other, making it impossible to successfully complete any of the puzzles. This is called a depletion trap. If the box is only shaken and there is no real control over individual pieces, these traps occur at random. Overcoming these random depletion traps is an important challenge when assembling nanostructures and other artificial molecules designed by humans without wasting many, potentially expensive, components. Previous studies have shown that when multiple copies of the same structure are assembled simultaneously, slowing the rate of initiation increases the yield of correctly-made structures. This prevents new structures from stealing pieces from existing structures before they are fully completed. Now, Gartner, Graf, Wilke et al. have used a mathematical model to show that changing the way initiation is delayed leads to different yields. This was especially true for small systems where fluctuations in the availability of the different pieces strongly enhanced the initiation of new structures. In these cases, the self-assembly process terminated undesirably with many incomplete structures. Nanostructures have various applications ranging from drug delivery to robotics. These findings suggest that in order to efficiently assemble biological molecules, the concentrations of the different building blocks need to be tightly controlled. A question for further research is to investigate strategies that reduce fluctuations in the availability of the building blocks to develop more efficient assembly protocols.
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Affiliation(s)
- Florian M Gartner
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, München, Germany
| | - Isabella R Graf
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, München, Germany
| | - Patrick Wilke
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, München, Germany
| | - Philipp M Geiger
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, München, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, München, Germany
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Maassen SJ, Huskens J, Cornelissen JJLM. Elucidating the Thermodynamic Driving Forces of Polyanion-Templated Virus-like Particle Assembly. J Phys Chem B 2019; 123:9733-9741. [PMID: 31661278 PMCID: PMC6875872 DOI: 10.1021/acs.jpcb.9b06258] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2019] [Revised: 10/01/2019] [Indexed: 01/09/2023]
Abstract
A virus in its most simple form is comprised of a protein capsid that surrounds and protects the viral genome. The self-assembly of such structures, however, is a highly complex, multiprotein, multiinteraction process and has been a topic of study for a number of years. This self-assembly process is driven by the (mainly electrostatic) interaction between the capsid proteins (CPs) and the genome as well as by the protein-protein interactions, which primarily rely on hydrophobic interactions. Insight in the thermodynamics that is involved in virus and virus-like particle (VLP) formation is crucial in the detailed understanding of this complex assembly process. Therefore, we studied the assembly of CPs of the cowpea chlorotic mottle virus (CCMV) templated by polyanionic species (cargo), that is, single-stranded DNA (ssDNA), and polystyrene sulfonate (PSS) using isothermal titration calorimetry. By separating the electrostatic CP-cargo interaction from the full assembly interaction, we conclude that CP-CP interactions cause an enthalpy change of -3 to -4 kcal mol-1 CP. Furthermore, we quantify that upon reducing the CP-CP interaction, in the case of CCMV by increasing the pH to 7, the CP-cargo starts to dominate VLP formation. This is highlighted by the three times higher affinity between CP and PSS compared to CP and ssDNA, resulting in the disassembly of CCMV at neutral pH in the presence of PSS to yield PSS-filled VLPs.
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Affiliation(s)
- Stan J. Maassen
- Laboratory
of Biomolecular Nanotechnology, MESA+ Institute for Nanotechnology and Molecular NanoFabrication
Group, MESA+ Institute for Nanotechnology, University of Twente, Enschede 7500 AE, The Netherlands
| | - Jurriaan Huskens
- Laboratory
of Biomolecular Nanotechnology, MESA+ Institute for Nanotechnology and Molecular NanoFabrication
Group, MESA+ Institute for Nanotechnology, University of Twente, Enschede 7500 AE, The Netherlands
| | - Jeroen J. L. M. Cornelissen
- Laboratory
of Biomolecular Nanotechnology, MESA+ Institute for Nanotechnology and Molecular NanoFabrication
Group, MESA+ Institute for Nanotechnology, University of Twente, Enschede 7500 AE, The Netherlands
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30
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Mesoscale model of the assembly and cross-linking of HPV virus-like particles. Virology 2019; 537:53-64. [PMID: 31450047 DOI: 10.1016/j.virol.2019.08.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Revised: 08/16/2019] [Accepted: 08/19/2019] [Indexed: 11/22/2022]
Abstract
We present a novel kinetic Monte Carlo model to simulate the real process time-scale of the assembly of Human Papillomavirus (HPV) virus-like particles (VLPs) incorporating the formation of intercapsomeric disulfide bonds. The objective was to develop insights into the underlying mechanisms of HPV VLP assembly and cross-linking during in vitro production of the HPV vaccine. The model integrates actual experimental data and detailed information of VLP geometrical structure in microscopic mechanistic steps. The principal novelty of this model is in the concurrent simulation of VLP assembly and cross-linking including a variable for spatial angular arrangement of capsomeres during their assembly that affects the overall rates of VLP assembly and cross-linking. The cross-linking modeled by using the mechanistic probability rules between involved cysteine residues. The model was utilized to better understand the actual process data and check on the hypothesis related to factors affecting the rates of HPV growth and maturation.
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31
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Asor R, Selzer L, Schlicksup CJ, Zhao Z, Zlotnick A, Raviv U. Assembly Reactions of Hepatitis B Capsid Protein into Capsid Nanoparticles Follow a Narrow Path through a Complex Reaction Landscape. ACS NANO 2019; 13:7610-7626. [PMID: 31173689 PMCID: PMC7243059 DOI: 10.1021/acsnano.9b00648] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
For many viruses, capsids (biological nanoparticles) assemble to protect genetic material and dissociate to release their cargo. To understand these contradictory properties, we analyzed capsid assembly for hepatitis B virus; an endemic pathogen with an icosahedral, 120-homodimer capsid. We used solution X-ray scattering to examine trapped and equilibrated assembly reactions. To fit experimental results, we generated a library of distinct intermediates, selected by umbrella sampling of Monte Carlo simulations. The number of possible capsid intermediates is immense, ∼1030, yet assembly reactions are rapid and completed with high fidelity. If the huge number of possible intermediates were actually present, maximum entropy analysis shows that assembly reactions would be blocked by an entropic barrier, resulting in incomplete nanoparticles. When an energetic term was applied to select the stable species that dominated the reaction mixture, we found only a few hundred intermediates, mapping out a narrow path through the immense reaction landscape. This is a solution to a viral application of the Levinthal paradox. With the correct energetic term, the match between predicted intermediates and scattering data was striking. The grand canonical free energy landscape for assembly, calibrated by our experimental results, supports a detailed analysis of this complex reaction. There is a narrow range of energies that supports on-path assembly. If association energy is too weak or too strong, progressively more intermediates will be entropically blocked, spilling into paths leading to dissociation or trapped incomplete nanoparticles, respectively. These results are relevant to many viruses and provide a basis for simplifying assembly models and identifying new targets for antiviral intervention. They provide a basis for understanding and designing biological and abiological self-assembly reactions.
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Affiliation(s)
- Roi Asor
- Institute of Chemistry and the Center for Nanoscience and Nanotechnology , The Hebrew University of Jerusalem , Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401 , Israel
| | - Lisa Selzer
- Department of Molecular and Cellular Biochemistry , Indiana University , Bloomington , Indiana 47405 , United States
- Department of Genetics , Stanford University School of Medicine , Stanford , California 94305 , United States
| | - Christopher John Schlicksup
- Department of Molecular and Cellular Biochemistry , Indiana University , Bloomington , Indiana 47405 , United States
| | - Zhongchao Zhao
- Department of Molecular and Cellular Biochemistry , Indiana University , Bloomington , Indiana 47405 , United States
| | - Adam Zlotnick
- Department of Molecular and Cellular Biochemistry , Indiana University , Bloomington , Indiana 47405 , United States
| | - Uri Raviv
- Institute of Chemistry and the Center for Nanoscience and Nanotechnology , The Hebrew University of Jerusalem , Edmond J. Safra Campus, Givat Ram, Jerusalem 9190401 , Israel
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32
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Abstract
In the self-assembly process which drives the formation of cellular membranes, micelles, and capsids, a collection of separated subunits spontaneously binds together to form functional and more ordered structures. In this work, we study the statistical physics of self-assembly in a simpler scenario: the formation of dimers from a system of monomers. The properties of the model allow us to frame the microstate counting as a combinatorial problem whose solution leads to an exact partition function. From the associated equilibrium conditions, we find that such dimer systems come in two types: "search-limited" and "combinatorics-limited," only the former of which has states where partial assembly can be dominated by correct contacts. Using estimates of biophysical quantities in systems of single-stranded DNA dimerization, transcription factor and DNA interactions, and protein-protein interactions, we find that all of these systems appear to be of the search-limited type, i.e., their fully correct dimerization regimes are more limited by the ability of monomers to find one another in the constituent volume than by the combinatorial disadvantage of correct dimers. We derive the parameter requirements for fully correct dimerization and find that rather than the ratio of particle number and volume (i.e., number density) being the relevant quantity, it is the product of particle diversity and volume that is constrained. Ultimately, this work contributes to an understanding of self-assembly by using the simple case of a system of dimers to analytically study the combinatorics of assembly.
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Affiliation(s)
- Mobolaji Williams
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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33
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Abstract
AbstractThe aggregation of the 11 residue long NACore peptide segment of α-synuclein (68-GAVVTGVTAVA-78) has been investigated using a combination of cryogenic transmission electron microscopy (cryo-TEM), small- and wide-angle X-ray scattering, and spectroscopy techniques. The aqueous peptide solubility is pH dependent, and aggregation was triggered by a pH quench from pH 11.3 to approximately pH 8 or 6, where the average peptide net charge is weakly negative (pH 8), or essentially zero (pH 6). Cryo-TEM shows the presence of long and stiff fibrillar aggregates at both pH, that are built up from β-sheets, as demonstrated by circular dichroism spectroscopy and thioflavin T fluorescence. The fibrils are crystalline, with a wide angle X-ray diffraction pattern that is consistent with a previously determined crystal structure of NACore. Of particular note is the cryo-TEM observation of small globular shaped aggregates, of the order of a few nanometers in size, adsorbed onto the surface of already formed fibrils at pH 6. The fibrillation kinetics is slow, and occurs on the time scale of days. Similarly slow kinetics is observed at both pH, but slightly slower at pH 6, even though the peptide solubility is here expected to be lower. The observation of the small globular shaped aggregates, together with the associated kinetics, could be highly relevant in relation to mechanisms of secondary nucleation and oligomer formation in amyloid systems.
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34
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Whitelam S. Strong bonds and far-from-equilibrium conditions minimize errors in lattice-gas growth. J Chem Phys 2018; 149:104902. [DOI: 10.1063/1.5034789] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Affiliation(s)
- Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
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35
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Mohajerani F, Hagan MF. The role of the encapsulated cargo in microcompartment assembly. PLoS Comput Biol 2018; 14:e1006351. [PMID: 30063715 PMCID: PMC6086489 DOI: 10.1371/journal.pcbi.1006351] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2018] [Revised: 08/10/2018] [Accepted: 07/10/2018] [Indexed: 11/19/2022] Open
Abstract
Bacterial microcompartments are large, roughly icosahedral shells that assemble around enzymes and reactants involved in certain metabolic pathways in bacteria. Motivated by microcompartment assembly, we use coarse-grained computational and theoretical modeling to study the factors that control the size and morphology of a protein shell assembling around hundreds to thousands of molecules. We perform dynamical simulations of shell assembly in the presence and absence of cargo over a range of interaction strengths, subunit and cargo stoichiometries, and the shell spontaneous curvature. Depending on these parameters, we find that the presence of a cargo can either increase or decrease the size of a shell relative to its intrinsic spontaneous curvature, as seen in recent experiments. These features are controlled by a balance of kinetic and thermodynamic effects, and the shell size is assembly pathway dependent. We discuss implications of these results for synthetic biology efforts to target new enzymes to microcompartment interiors.
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Affiliation(s)
- Farzaneh Mohajerani
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts, United States of America
| | - Michael F. Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts, United States of America
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36
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Newton AC, Groenewold J, Kegel WK, Bolhuis PG. The role of multivalency in the association kinetics of patchy particle complexes. J Chem Phys 2018. [PMID: 28641424 DOI: 10.1063/1.4984966] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Association and dissociation of particles are elementary steps in many natural and technological relevant processes. For many such processes, the presence of multiple binding sites is essential. For instance, protein complexes and regular structures such as virus shells are formed from elementary building blocks with multiple binding sites. Here we address a fundamental question concerning the role of multivalency of binding sites in the association kinetics of such complexes. Using single replica transition interface sampling simulations, we investigate the influence of the multivalency on the binding kinetics and the association mechanism of patchy particles that form polyhedral clusters. When the individual bond strength is fixed, the kinetics naturally is very dependent on the multivalency, with dissociation rate constants exponentially decreasing with the number of bonds. In contrast, we find that when the total bond energy per particle is kept constant, association and dissociation rate constants turn out rather independent of multivalency, although of course still very dependent on the total energy. The association and dissociation mechanisms, however, depend on the presence and nature of the intermediate states. For instance, pathways that visit intermediate states are less prevalent for particles with five binding sites compared to the case of particles with only three bonds. The presence of intermediate states can lead to kinetic trapping and malformed aggregates. We discuss implications for natural forming complexes such as virus shells and for the design of artificial colloidal patchy particles.
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Affiliation(s)
- Arthur C Newton
- Van't Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Jan Groenewold
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands
| | - Willem K Kegel
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands
| | - Peter G Bolhuis
- Van't Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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37
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Tang X, Feula A, Baker BC, Melia K, Hermida Merino D, Hamley IW, Buckley CP, Hayes W, Siviour CR. A dynamic supramolecular polyurethane network whose mechanical properties are kinetically controlled. POLYMER 2017. [DOI: 10.1016/j.polymer.2017.11.005] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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38
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Chen J, Chevreuil M, Combet S, Lansac Y, Tresset G. Investigating the thermal dissociation of viral capsid by lattice model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:474001. [PMID: 29098985 PMCID: PMC7104912 DOI: 10.1088/1361-648x/aa8d88] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/31/2017] [Revised: 09/08/2017] [Accepted: 09/19/2017] [Indexed: 06/07/2023]
Abstract
The dissociation of icosahedral viral capsids was investigated by a homogeneous and a heterogeneous lattice model. In thermal dissociation experiments with cowpea chlorotic mottle virus and probed by small-angle neutron scattering, we observed a slight shrinkage of viral capsids, which can be related to the strengthening of the hydrophobic interaction between subunits at increasing temperature. By considering the temperature dependence of hydrophobic interaction in the homogeneous lattice model, we were able to give a better estimate of the effective charge. In the heterogeneous lattice model, two sets of lattice sites represented different capsid subunits with asymmetric interaction strengths. In that case, the dissociation of capsids was found to shift from a sharp one-step transition to a gradual two-step transition by weakening the hydrophobic interaction between AB and CC subunits. We anticipate that such lattice models will shed further light on the statistical mechanics underlying virus assembly and disassembly.
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Affiliation(s)
- Jingzhi Chen
- Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France
| | - Maelenn Chevreuil
- Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France
| | - Sophie Combet
- Laboratoire Léon Brillouin (LLB), UMR 12 CEA-CNRS, CEA-Saclay, F-91191 Gif-sur-Yvette Cedex, France
| | - Yves Lansac
- Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France
- GREMAN, CNRS, Université François Rabelais, 73200 Tours, France
| | - Guillaume Tresset
- Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France
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39
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Immature HIV-1 lattice assembly dynamics are regulated by scaffolding from nucleic acid and the plasma membrane. Proc Natl Acad Sci U S A 2017; 114:E10056-E10065. [PMID: 29114055 DOI: 10.1073/pnas.1706600114] [Citation(s) in RCA: 63] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
The packaging and budding of Gag polyprotein and viral RNA is a critical step in the HIV-1 life cycle. High-resolution structures of the Gag polyprotein have revealed that the capsid (CA) and spacer peptide 1 (SP1) domains contain important interfaces for Gag self-assembly. However, the molecular details of the multimerization process, especially in the presence of RNA and the cell membrane, have remained unclear. In this work, we investigate the mechanisms that work in concert between the polyproteins, RNA, and membrane to promote immature lattice growth. We develop a coarse-grained (CG) computational model that is derived from subnanometer resolution structural data. Our simulations recapitulate contiguous and hexameric lattice assembly driven only by weak anisotropic attractions at the helical CA-SP1 junction. Importantly, analysis from CG and single-particle tracking photoactivated localization (spt-PALM) trajectories indicates that viral RNA and the membrane are critical constituents that actively promote Gag multimerization through scaffolding, while overexpression of short competitor RNA can suppress assembly. We also find that the CA amino-terminal domain imparts intrinsic curvature to the Gag lattice. As a consequence, immature lattice growth appears to be coupled to the dynamics of spontaneous membrane deformation. Our findings elucidate a simple network of interactions that regulate the early stages of HIV-1 assembly and budding.
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40
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Abstract
Molecular self-assembly is the dominant form of chemical reaction in living systems, yet efforts at systems biology modeling are only beginning to appreciate the need for and challenges to accurate quantitative modeling of self-assembly. Self-assembly reactions are essential to nearly every important process in cell and molecular biology and handling them is thus a necessary step in building comprehensive models of complex cellular systems. They present exceptional challenges, however, to standard methods for simulating complex systems. While the general systems biology world is just beginning to deal with these challenges, there is an extensive literature dealing with them for more specialized self-assembly modeling. This review will examine the challenges of self-assembly modeling, nascent efforts to deal with these challenges in the systems modeling community, and some of the solutions offered in prior work on self-assembly specifically. The review concludes with some consideration of the likely role of self-assembly in the future of complex biological system models more generally.
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Affiliation(s)
- Marcus Thomas
- Computational Biology Department, Carnegie Mellon University, 4400 Fifth Avenue, Pittsburgh, PA 15213, United States of America. Joint Carnegie Mellon University/University of Pittsburgh Ph.D. Program in Computational Biology, 4400 Fifth Avenue, Pittsburgh, PA 15213, United States of America
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41
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Pires RH, Saraiva MJ, Damas AM, Kellermayer MSZ. Force spectroscopy reveals the presence of structurally modified dimers in transthyretin amyloid annular oligomers. J Mol Recognit 2016; 30. [PMID: 27808434 DOI: 10.1002/jmr.2587] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2016] [Revised: 09/21/2016] [Accepted: 09/30/2016] [Indexed: 12/17/2022]
Abstract
Toxicity in amyloidogenic protein misfolding disorders is thought to involve intermediate states of aggregation associated with the formation of amyloid fibrils. Despite their relevance, the heterogeneity and transience of these oligomers have placed great barriers in our understanding of their structural properties. Among amyloid intermediates, annular oligomers or annular protofibrils have raised considerable interest because they may contribute to a mechanism of cellular toxicity via membrane permeation. Here we investigated, by using AFM force spectroscopy, the structural detail of amyloid annular oligomers from transthyretin (TTR), a protein involved in systemic and neurodegenerative amyloidogenic disorders. Manipulation was performed in situ, in the absence of molecular handles and using persistence length-fit values to select relevant curves. Force curves reveal the presence of dimers in TTR annular oligomers that unfold via a series of structural intermediates. This is in contrast with the manipulation of native TTR that was more often manipulated over length scales compatible with a TTR monomer and without unfolding intermediates. Imaging and force spectroscopy data suggest that dimers are formed by the assembly of monomers in a head-to-head orientation with a nonnative interface along their β-strands. Furthermore, these dimers stack through nonnative contacts that may enhance the stability of the misfolded structure.
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Affiliation(s)
- Ricardo H Pires
- Department of Biophysics and Radiation Biology, Semmelweis University, Budapest, Hungary.,Institute for Molecular and Cell Biology (IBMC), Porto, Portugal
| | - Maria J Saraiva
- Institute for Molecular and Cell Biology (IBMC), Porto, Portugal.,Instituto de Ciências Biomédicas de Abel Salazar (ICBAS), Universidade do Porto, Porto, Portugal
| | - Ana M Damas
- Institute for Molecular and Cell Biology (IBMC), Porto, Portugal.,Instituto de Ciências Biomédicas de Abel Salazar (ICBAS), Universidade do Porto, Porto, Portugal
| | - Miklós S Z Kellermayer
- Department of Biophysics and Radiation Biology, Semmelweis University, Budapest, Hungary.,MTA-SE Molecular Biophysics Research Group, Budapest, Hungary
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42
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Rochal SB, Konevtsova OV, Myasnikova AE, Lorman VL. Hidden symmetry of small spherical viruses and organization principles in "anomalous" and double-shelled capsid nanoassemblies. NANOSCALE 2016; 8:16976-16988. [PMID: 27714069 DOI: 10.1039/c6nr04930c] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We propose the principles of structural organization in spherical nanoassemblies with icosahedral symmetry constituted by asymmetric protein molecules. The approach modifies the paradigmatic geometrical Caspar and Klug (CK) model of icosahedral viral capsids and demonstrates the common origin of both the "anomalous" and conventional capsid structures. In contrast to all previous models of "anomalous" viral capsids the proposed modified model conserves the basic structural principles of the CK approach and reveals the common hidden symmetry underlying all small viral shells. We demonstrate the common genesis of the "anomalous" and conventional capsids and explain their structures in the same frame. The organization principles are derived from the group theory analysis of the positional order on the spherical surface. The relationship between the modified CK geometrical model and the theory of two-dimensional spherical crystallization is discussed. We also apply the proposed approach to complex double-shelled capsids and capsids with protruding knob-like proteins. The introduced notion of commensurability for the concentric nanoshells explains the peculiarities of their organization and helps to predict analogous, but yet undiscovered, double-shelled viral capsid nanostructures.
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Affiliation(s)
- S B Rochal
- Faculty of Physics, Southern Federal University, 5 Zorge str., 344090 Rostov-on-Don, Russia.
| | - O V Konevtsova
- Faculty of Physics, Southern Federal University, 5 Zorge str., 344090 Rostov-on-Don, Russia.
| | - A E Myasnikova
- Faculty of Physics, Southern Federal University, 5 Zorge str., 344090 Rostov-on-Don, Russia.
| | - V L Lorman
- Laboratoire Charles Coulomb, UMR 5221 CNRS and Université Montpellier 2, pl. E. Bataillon, 34095 Montpellier, France
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43
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Mahalik JP, Brown KA, Cheng X, Fuentes-Cabrera M. Theoretical Study of the Initial Stages of Self-Assembly of a Carboxysome's Facet. ACS NANO 2016; 10:5751-8. [PMID: 26906087 DOI: 10.1021/acsnano.5b07805] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Bacterial microcompartments, BMCs, are organelles that exist within wide variety of bacteria and act as nanofactories. Among the different types of known BMCs, the carboxysome has been studied the most. The carboxysome plays an important role in the light-independent part of the photosynthesis process, where its icosahedral-like proteinaceous shell acts as a membrane that controls the transport of metabolites. Although a structural model exists for the carboxysome shell, it remains largely unknown how the shell proteins self-assemble. Understanding the self-assembly process can provide insights into how the shell affects the carboxysome's function and how it can be modified to create new functionalities, such as artificial nanoreactors and artificial protein membranes. Here, we describe a theoretical framework that employs Monte Carlo simulations with a coarse-grain potential that reproduces well the atomistic potential of mean force; employing this framework, we are able to capture the initial stages of the 2D self-assembly of CcmK2 hexamers, a major protein-shell component of the carboxysome's facet. The simulations reveal that CcmK2 hexamers self-assemble into clusters that resemble what was seen experimentally in 2D layers. Further analysis of the simulation results suggests that the 2D self-assembly of carboxysome's facets is driven by a nucleation-growth process, which in turn could play an important role in the hierarchical self-assembly of BMC shells in general.
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Affiliation(s)
| | - Kirsten A Brown
- Chemistry Department, Mercer University , 1501 Mercer University Drive, Macon, Georgia 31207, United States
| | - Xiaolin Cheng
- Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee , M407 Walters Life Sciences, 1414 Cumberland Avenue, Knoxville, Tennessee 37996, United States
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44
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Perlmutter JD, Mohajerani F, Hagan MF. Many-molecule encapsulation by an icosahedral shell. eLife 2016; 5. [PMID: 27166515 PMCID: PMC4947392 DOI: 10.7554/elife.14078] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2015] [Accepted: 05/10/2016] [Indexed: 12/31/2022] Open
Abstract
We computationally study how an icosahedral shell assembles around hundreds of molecules. Such a process occurs during the formation of the carboxysome, a bacterial microcompartment that assembles around many copies of the enzymes ribulose 1,5-bisphosphate carboxylase/ oxygenase and carbonic anhydrase to facilitate carbon fixation in cyanobacteria. Our simulations identify two classes of assembly pathways leading to encapsulation of many-molecule cargoes. In one, shell assembly proceeds concomitantly with cargo condensation. In the other, the cargo first forms a dense globule; then, shell proteins assemble around and bud from the condensed cargo complex. Although the model is simplified, the simulations predict intermediates and closure mechanisms not accessible in experiments, and show how assembly can be tuned between these two pathways by modulating protein interactions. In addition to elucidating assembly pathways and critical control parameters for microcompartment assembly, our results may guide the reengineering of viruses as nanoreactors that self-assemble around their reactants. DOI:http://dx.doi.org/10.7554/eLife.14078.001 Bacterial microcompartments are protein shells that are found inside bacteria and enclose enzymes and other chemicals required for certain biological reactions. For example, the carboxysome is a type of microcompartment that enables the bacteria to convert the products of photosynthesis into sugars. During the formation of a microcompartment, the outer protein shell assembles around hundreds of enzymes and chemicals. This formation process is tightly controlled and involves multiple interactions between the shell proteins and the cargo – the enzymes and other reaction ingredients – they will enclose. Understanding how to control which enzymes are encapsulated within microcompartments could help researchers to re-engineer the microcompartments so that they contain drugs or other useful products. Recent studies have used microscopy to visualize how microcompartments are assembled. However, most of the intermediate structures that form during assembly are too small and short-lived to be seen. It has therefore not been possible to explore in detail how shell proteins collect the necessary cargo and then assemble into an ordered shell with the cargo on the inside. Experiments alone are probably not enough to understand the process, especially since microcompartment assembly can currently only be studied within live cells or cellular extract. Within these complex environments it is difficult to determine the effect of any individual factor on the overall assembly process. Perlmutter, Mohajerani and Hagan have now taken a different approach by developing computational and theoretical models to explore how microcompartments assemble. Computer simulations showed that microcompartments could assemble by two pathways. In one pathway, the protein shell and cargo coalesce at the same time. In the other pathway, the cargo molecules first assemble into a large disordered complex, with the shell proteins attached on the outside. The shell proteins then assemble, carving out a piece of the cargo complex. The simulations showed that many factors affect how the shell assembles, such as the strengths of the interactions between the shell proteins and the cargo. They also identified a factor that controls how much cargo ends up inside the assembled shell. Perlmutter, Mohajerani and Hagan found that, in addition to revealing how microcompartments may assemble within their natural setting, the simulations provided guidance on how to re-engineer microcompartments to assemble around other components. This would enable researchers to create customizable compartments that self-assemble within bacteria or other host organisms, for example to carry out carbon fixation or make biofuels. A future challenge will be to investigate other aspects of microcompartment assembly, such as the factors that control the size of these compartments. DOI:http://dx.doi.org/10.7554/eLife.14078.002
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Affiliation(s)
- Jason D Perlmutter
- Martin Fisher School of Physics, Brandeis University, Waltham, United States
| | - Farzaneh Mohajerani
- Martin Fisher School of Physics, Brandeis University, Waltham, United States
| | - Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, United States
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45
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Abstract
During the life cycle of a virus, viral proteins and other components self-assemble to form an ordered protein shell called a capsid. This assembly process is subject to multiple competing constraints, including the need to form a thermostable shell while avoiding kinetic traps. It has been proposed that viral assembly satisfies these constraints through allosteric regulation, including the interconversion of capsid proteins among conformations with different propensities for assembly. In this article, we use computational and theoretical modeling to explore how such allostery affects the assembly of icosahedral shells. We simulate assembly under a wide range of protein concentrations, protein binding affinities, and two different mechanisms of allosteric control. We find that above a threshold strength of allosteric control, assembly becomes robust over a broad range of subunit binding affinities and concentrations, allowing the formation of highly thermostable capsids. Our results suggest that allostery can significantly shift the range of protein binding affinities that lead to successful assembly and thus should be taken into account in models that are used to estimate interaction parameters from experimental data.
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Affiliation(s)
- Guillermo R Lazaro
- Martin Fisher School of Physics, Brandeis University , Waltham, Massachusetts 02454, United States
| | - Michael F Hagan
- Martin Fisher School of Physics, Brandeis University , Waltham, Massachusetts 02454, United States
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46
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Li R, Zhang J, Tan R, Gerdes F, Luo Z, Xu H, Hollingsworth JA, Klinke C, Chen O, Wang Z. Competing Interactions between Various Entropic Forces toward Assembly of Pt3Ni Octahedra into a Body-Centered Cubic Superlattice. NANO LETTERS 2016; 16:2792-9. [PMID: 26977777 DOI: 10.1021/acs.nanolett.6b00564] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Anisotropic nanocrystal assembled supercrystals with open superlattices (SLs) manifest novel and unique properties, but poor understanding of the nucleation/growth mechanisms limits their design and fabrication for practical applications. Using highly anisotropic Pt3Ni octahedral nanocrystals, we have grown large single supercrystals with an open body-centered cubic (bcc) superlattice that has a low filling factor of 26.8%. Synchrotron-based X-ray structural reconstruction fully revealed the coherence of translational and orientational orderings and determined that the constituent octahedra arrange themselves with the vertex-to-vertex and face-to-face configurations along the SL[100] and SL[111] directions, respectively. The large face-to-face separation and flexible vertex-to-vertex elastic contact provided the rattle space and supporting axis for local rotations of Pt3Ni octahedra within the bcc superlattice. Development of orientational disordering along with robust preservation of translational ordering during the heating process of a supercrystal in the oleic acid wetting environment confirmed the dominance of rotational entropy of hard octahedra in the formation of the open bcc superlattice. Ultimate achievement of dynamic equilibrium between the vertex-oriented elastic repulsions and the face-oriented attractions of surface-coating ligands governs the structural and mechanical stability of the supercrystal. This discovery provides significant insights into the design and control of geometrical shapes for the fabrication of highly anisotropic nanocrystals into desired open superlattices with tailored optical and electronic properties.
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Affiliation(s)
- Ruipeng Li
- Cornell High Energy Synchrotron Source, Cornell University , Ithaca, New York 14850, United States
| | - Jun Zhang
- State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum , Qingdao 266580, China
| | - Rui Tan
- Department of Chemistry, Brown University , Providence, Rhode Island 02912, United States
| | - Frauke Gerdes
- Institute of Physical Chemistry, University of Hamburg , 20146 Hamburg, Germany
| | - Zhiping Luo
- Department of Chemistry and Physics, Fayetteville State University , Fayetteville, North Carolina 28301, United States
| | | | | | - Christian Klinke
- Institute of Physical Chemistry, University of Hamburg , 20146 Hamburg, Germany
| | - Ou Chen
- Department of Chemistry, Brown University , Providence, Rhode Island 02912, United States
| | - Zhongwu Wang
- Cornell High Energy Synchrotron Source, Cornell University , Ithaca, New York 14850, United States
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47
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Hagan MF, Zandi R. Recent advances in coarse-grained modeling of virus assembly. Curr Opin Virol 2016; 18:36-43. [PMID: 27016708 DOI: 10.1016/j.coviro.2016.02.012] [Citation(s) in RCA: 75] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2016] [Accepted: 02/29/2016] [Indexed: 01/08/2023]
Affiliation(s)
- Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA.
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA.
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48
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Abstract
Nanomanufacturing, the commercially scalable and economically sustainable mass production of nanoscale materials and devices, represents the tangible outcome of the nanotechnology revolution. In contrast to those used in nanofabrication for research purposes, nanomanufacturing processes must satisfy the additional constraints of cost, throughput, and time to market. Taking silicon integrated circuit manufacturing as a baseline, we consider the factors involved in matching processes with products, examining the characteristics and potential of top-down and bottom-up processes, and their combination. We also discuss how a careful assessment of the way in which function can be made to follow form can enable high-volume manufacturing of nanoscale structures with the desired useful, and exciting, properties.
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Affiliation(s)
- J. Alexander Liddle
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899
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Harms ZD, Selzer L, Zlotnick A, Jacobson SC. Monitoring Assembly of Virus Capsids with Nanofluidic Devices. ACS NANO 2015; 9:9087-96. [PMID: 26266555 PMCID: PMC4753561 DOI: 10.1021/acsnano.5b03231] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Virus assembly is a coordinated process in which typically hundreds of subunits react to form complex, symmetric particles. We use resistive-pulse sensing to characterize the assembly of hepatitis B virus core protein dimers into T = 3 and T = 4 icosahedral capsids. This technique counts and sizes intermediates and capsids in real time, with single-particle sensitivity, and at biologically relevant concentrations. Other methods are not able to produce comparable real-time, single-particle observations of assembly reactions below, near, and above the pseudocritical dimer concentration, at which the dimer and capsid concentrations are approximately equal. Assembly reactions across a range of dimer concentrations reveal three distinct patterns. At dimer concentrations as low as 50 nM, well below the pseudocritical dimer concentration of 0.5 μM, we observe a switch in the ratio of T = 3 to T = 4 capsids, which increases with decreasing dimer concentration. Far above the pseudocritical dimer concentration, kinetically trapped, incomplete T = 4 particles assemble rapidly, then slowly anneal into T = 4 capsids. At all dimer concentrations tested, T = 3 capsids form more rapidly than T = 4 capsids, suggesting distinct pathways for the two forms.
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Affiliation(s)
- Zachary D. Harms
- Department of Chemistry, Indiana University, Bloomington, IN 47405
| | - Lisa Selzer
- Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, IN 47405
| | - Adam Zlotnick
- Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, IN 47405
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The Role of Packaging Sites in Efficient and Specific Virus Assembly. J Mol Biol 2015; 427:2451-2467. [PMID: 25986309 DOI: 10.1016/j.jmb.2015.05.008] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2015] [Revised: 04/21/2015] [Accepted: 05/10/2015] [Indexed: 12/25/2022]
Abstract
During the life cycle of many single-stranded RNA viruses, including many human pathogens, a protein shell called the capsid spontaneously assembles around the viral genome. Understanding the mechanisms by which capsid proteins selectively assemble around the viral RNA amidst diverse host RNAs is a key question in virology. In one proposed mechanism, short sequences (packaging sites) within the genomic RNA promote rapid and efficient assembly through specific interactions with the capsid proteins. In this work, we develop a coarse-grained particle-based computational model for capsid proteins and RNA that represents protein-RNA interactions arising both from nonspecific electrostatics and from specific packaging site interactions. Using Brownian dynamics simulations, we explore how the efficiency and specificity of assembly depend on solution conditions (which control protein-protein and nonspecific protein-RNA interactions) and the strength and number of packaging sites. We identify distinct regions in parameter space in which packaging sites lead to highly specific assembly via different mechanisms and others in which packaging sites lead to kinetic traps. We relate these computational predictions to in vitro assays for specificity in which cognate viral RNAs compete against non-cognate RNAs for assembly by capsid proteins.
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