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Hayakawa D, Videbæk TE, Grason GM, Rogers WB. Symmetry-Guided Inverse Design of Self-Assembling Multiscale DNA Origami Tilings. ACS NANO 2024; 18:19169-19178. [PMID: 38981100 PMCID: PMC11271658 DOI: 10.1021/acsnano.4c04515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2024] [Revised: 06/21/2024] [Accepted: 06/24/2024] [Indexed: 07/11/2024]
Abstract
Recent advances enable the creation of nanoscale building blocks with complex geometries and interaction specificities for self-assembly. This nearly boundless design space necessitates design principles for defining the mutual interactions between multiple particle species to target a user-specified complex structure or pattern. In this article, we develop a symmetry-based method to generate the interaction matrices that specify the assembly of two-dimensional tilings, which we illustrate using equilateral triangles. By exploiting the allowed 2D symmetries, we develop an algorithmic approach by which any periodic 2D tiling can be generated from an arbitrarily large number of subunit species, notably addressing an unmet challenge of engineering 2D crystals with periodicities that can be arbitrarily larger than the subunit size. To demonstrate the utility of our design approach, we encode specific interactions between triangular subunits synthesized by DNA origami and show that we can guide their self-assembly into tilings with a wide variety of symmetries, using up to 12 unique species of triangles. By conjugating specific triangles with gold nanoparticles, we fabricate gold-nanoparticle supracrystals whose lattice parameter spans up to 300 nm. Finally, to generate economical design rules, we compare the design economy of various tilings. In particular, we show that (1) higher symmetries allow assembly of larger unit cells with fewer subunits and (2) linear supracrystals can be designed more economically using linear primitive unit cells. This work provides a simple algorithmic approach to designing periodic assemblies, aiding in the multiscale assembly of supracrystals of nanostructured "meta-atoms" with engineered plasmonic functions.
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Affiliation(s)
- Daichi Hayakawa
- Martin
A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Thomas E. Videbæk
- Martin
A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Gregory M. Grason
- Department
of Polymer Science and Engineering, University
of Massachusetts, Amherst, Massachusetts 01003, United States
| | - W. Benjamin Rogers
- Martin
A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
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Videbæk TE, Hayakawa D, Grason GM, Hagan MF, Fraden S, Rogers WB. Economical routes to size-specific assembly of self-closing structures. SCIENCE ADVANCES 2024; 10:eado5979. [PMID: 38959303 PMCID: PMC11221488 DOI: 10.1126/sciadv.ado5979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2024] [Accepted: 05/30/2024] [Indexed: 07/05/2024]
Abstract
Programmable self-assembly has seen an explosion in the diversity of synthetic crystalline materials, but developing strategies that target "self-limiting" assemblies has remained a challenge. Among these, self-closing structures, in which the local curvature defines the finite global size, are prone to polymorphism due to thermal bending fluctuations, a problem that worsens with increasing target size. Here, we show that assembly complexity can be used to eliminate this source of polymorphism in the assembly of tubules. Using many distinct components, we prune the local density of off-target geometries, increasing the selectivity of the tubule width and helicity to nearly 100%. We further show that by reducing the design constraints to target either the pitch or the width alone, fewer components are needed to reach complete selectivity. Combining experiments with theory, we reveal an economical limit, which determines the minimum number of components required to create arbitrary assembly sizes with full selectivity.
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Affiliation(s)
- Thomas E. Videbæk
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA
| | - Daichi Hayakawa
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA
| | - Gregory M. Grason
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003, USA
| | - Michael F. Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA
| | - Seth Fraden
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA
| | - W. Benjamin Rogers
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA
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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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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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Geometrically programmed self-limited assembly of tubules using DNA origami colloids. Proc Natl Acad Sci U S A 2022; 119:e2207902119. [PMID: 36252043 PMCID: PMC9618141 DOI: 10.1073/pnas.2207902119] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Nature is replete with self-assembled materials that have one or more self-limited dimensions, including shells, tubules, and fibers. Despite significant advances in making nanometer- and micrometer-scale subunits, the programmable assembly of similar self-limiting architectures from synthetic components has remained largely out of reach. In this article, we create geometrically programmed subunits using DNA origami and study their assembly into tubules with a self-limited width. We show that the average self-limited dimension can be tuned by changing the local curvature encoded in a single subunit. Exploiting the programmability of our system, we further test the tradeoffs between fidelity and complexity embodied by two paradigms for self-limited assembly: self-closure through programmed curvature and addressable assembly through programmed specific interactions. Self-assembly is one of the most promising strategies for making functional materials at the nanoscale, yet new design principles for making self-limiting architectures, rather than spatially unlimited periodic lattice structures, are needed. To address this challenge, we explore the tradeoffs between addressable assembly and self-closing assembly of a specific class of self-limiting structures: cylindrical tubules. We make triangular subunits using DNA origami that have specific, valence-limited interactions and designed binding angles, and we study their assembly into tubules that have a self-limited width that is much larger than the size of an individual subunit. In the simplest case, the tubules are assembled from a single component by geometrically programming the dihedral angles between neighboring subunits. We show that the tubules can reach many micrometers in length and that their average width can be prescribed through the dihedral angles. We find that there is a distribution in the width and the chirality of the tubules, which we rationalize by developing a model that considers the finite bending rigidity of the assembled structure as well as the mechanism of self-closure. Finally, we demonstrate that the distributions of tubules can be further sculpted by increasing the number of subunit species, thereby increasing the assembly complexity, and demonstrate that using two subunit species successfully reduces the number of available end states by half. These results help to shed light on the roles of assembly complexity and geometry in self-limited assembly and could be extended to other self-limiting architectures, such as shells, toroids, or triply periodic frameworks.
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Mohajerani F, Tyukodi B, Schlicksup CJ, Hadden-Perilla JA, Zlotnick A, Hagan MF. Multiscale Modeling of Hepatitis B Virus Capsid Assembly and Its Dimorphism. ACS NANO 2022; 16:13845-13859. [PMID: 36054910 PMCID: PMC10273259 DOI: 10.1021/acsnano.2c02119] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Hepatitis B virus (HBV) is an endemic, chronic virus that leads to 800000 deaths per year. Central to the HBV lifecycle, the viral core has a protein capsid assembled from many copies of a single protein. The capsid protein adopts different (quasi-equivalent) conformations to form icosahedral capsids containing 180 or 240 proteins: T = 3 or T = 4, respectively, in Caspar-Klug nomenclature. HBV capsid assembly has become an important target for recently developed antivirals; nonetheless, the assembly pathways and mechanisms that control HBV dimorphism remain unclear. We describe computer simulations of the HBV assembly, using a coarse-grained model that has parameters learned from all-atom molecular dynamics simulations of a complete HBV capsid and yet is computationally tractable. Dynamical simulations with the resulting model reproduce experimental observations of HBV assembly pathways and products. By constructing Markov state models and employing transition path theory, we identify pathways leading to T = 3, T = 4, and other experimentally observed capsid morphologies. The analysis shows that capsid polymorphism is promoted by the low HBV capsid bending modulus, where the key factors controlling polymorphism are the conformational energy landscape and protein-protein binding affinities.
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Affiliation(s)
- Farzaneh Mohajerani
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts02453, United States
| | - Botond Tyukodi
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts02453, United States
- Department of Physics, Babeş-Bolyai University, 400084Cluj-Napoca, Romania
| | - Christopher J Schlicksup
- Molecular and Cellular Biochemistry Department, Indiana University, Bloomington, Indiana47405, United States
| | - Jodi A Hadden-Perilla
- Department of Chemistry & Biochemistry, University of Delaware, Newark, Delaware19716, United States
| | - Adam Zlotnick
- Molecular and Cellular Biochemistry Department, Indiana University, Bloomington, Indiana47405, United States
| | - Michael F Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts02453, United States
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Fang H, Tyukodi B, Rogers WB, Hagan MF. Polymorphic self-assembly of helical tubules is kinetically controlled. SOFT MATTER 2022; 18:6716-6728. [PMID: 36039801 PMCID: PMC9472595 DOI: 10.1039/d2sm00679k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 08/12/2022] [Indexed: 06/15/2023]
Abstract
In contrast to most self-assembling synthetic materials, which undergo unbounded growth, many biological self-assembly processes are self-limited. That is, the assembled structures have one or more finite dimensions that are much larger than the size scale of the individual monomers. In many such cases, the finite dimension is selected by a preferred curvature of the monomers, which leads to self-closure of the assembly. In this article, we study an example class of self-closing assemblies: cylindrical tubules that assemble from triangular monomers. By combining kinetic Monte Carlo simulations, free energy calculations, and simple theoretical models, we show that a range of programmable size scales can be targeted by controlling the intricate balance between the preferred curvature of the monomers and their interaction strengths. However, their assembly is kinetically controlled-the tubule morphology is essentially fixed shortly after closure, resulting in a distribution of tubule widths that is significantly broader than the equilibrium distribution. We develop a simple kinetic model based on this observation and the underlying free-energy landscape of assembling tubules that quantitatively describes the distributions. Our results are consistent with recent experimental observations of tubule assembly from triangular DNA origami monomers. The modeling framework elucidates design principles for assembling self-limited structures from synthetic components, such as artificial microtubules that have a desired width and chirality.
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Affiliation(s)
- Huang Fang
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
| | - Botond Tyukodi
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
- Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
| | - W Benjamin Rogers
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
| | - Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
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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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