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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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Osat S, Metson J, Kardar M, Golestanian R. Escaping Kinetic Traps Using Nonreciprocal Interactions. PHYSICAL REVIEW LETTERS 2024; 133:028301. [PMID: 39073937 DOI: 10.1103/physrevlett.133.028301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 06/10/2024] [Indexed: 07/31/2024]
Abstract
Kinetic traps are a notorious problem in equilibrium statistical mechanics, where temperature quenches ultimately fail to bring the system to low energy configurations. Using multifarious self-assembly as a model system, we introduce a mechanism to escape kinetic traps by utilizing nonreciprocal interactions between components. Introducing nonequilibrium effects offered by broken action-reaction symmetry in the system pushes the trajectory of the system out of arrested dynamics. The dynamics of the model is studied using tools from the physics of interfaces and defects. Our proposal can find applications in self-assembly, glassy systems, and systems with arrested dynamics to facilitate escape from local minima in rough energy landscapes.
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Jhaveri A, Loggia S, Qian Y, Johnson ME. Discovering optimal kinetic pathways for self-assembly using automatic differentiation. Proc Natl Acad Sci U S A 2024; 121:e2403384121. [PMID: 38691585 PMCID: PMC11087789 DOI: 10.1073/pnas.2403384121] [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: 02/22/2024] [Accepted: 04/03/2024] [Indexed: 05/03/2024] Open
Abstract
Macromolecular complexes are often composed of diverse subunits. The self-assembly of these subunits is inherently nonequilibrium and must avoid kinetic traps to achieve high yield over feasible timescales. We show how the kinetics of self-assembly benefits from diversity in subunits because it generates an expansive parameter space that naturally improves the "expressivity" of self-assembly, much like a deeper neural network. By using automatic differentiation algorithms commonly used in deep learning, we searched the parameter spaces of mass-action kinetic models to identify classes of kinetic protocols that mimic biological solutions for productive self-assembly. Our results reveal how high-yield complexes that easily become kinetically trapped in incomplete intermediates can instead be steered by internal design of rate-constants or external and active control of subunits to efficiently assemble. Internal design of a hierarchy of subunit binding rates generates self-assembly that can robustly avoid kinetic traps for all concentrations and energetics, but it places strict constraints on selection of relative rates. External control via subunit titration is more versatile, avoiding kinetic traps for any system without requiring molecular engineering of binding rates, albeit less efficiently and robustly. We derive theoretical expressions for the timescales of kinetic traps, and we demonstrate our optimization method applies not just for design but inference, extracting intersubunit binding rates from observations of yield-vs.-time for a heterotetramer. Overall, we identify optimal kinetic protocols for self-assembly as a powerful mechanism to achieve efficient and high-yield assembly in synthetic systems whether robustness or ease of "designability" is preferred.
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Affiliation(s)
- Adip Jhaveri
- Thomas C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD21218
| | - Spencer Loggia
- Thomas C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD21218
| | - Yian Qian
- Thomas C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD21218
| | - Margaret E. Johnson
- Thomas C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD21218
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Jhaveri A, Loggia S, Qian Y, Johnson ME. Discovering optimal kinetic pathways for self-assembly using automatic differentiation. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.08.30.555551. [PMID: 37693527 PMCID: PMC10491160 DOI: 10.1101/2023.08.30.555551] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/12/2023]
Abstract
During self-assembly of macromolecules ranging from ribosomes to viral capsids, the formation of long-lived intermediates or kinetic traps can dramatically reduce yield of the functional products. Understanding biological mechanisms for avoiding traps and efficiently assembling is essential for designing synthetic assembly systems, but learning optimal solutions requires numerical searches in high-dimensional parameter spaces. Here, we exploit powerful automatic differentiation algorithms commonly employed by deep learning frameworks to optimize physical models of reversible self-assembly, discovering diverse solutions in the space of rate constants for 3-7 subunit complexes. We define two biologically-inspired protocols that prevent kinetic trapping through either internal design of subunit binding kinetics or external design of subunit titration in time. Our third protocol acts to recycle intermediates, mimicking energy-consuming enzymes. Preventative solutions via interface design are the most efficient and scale better with more subunits, but external control via titration or recycling are effective even for poorly evolved binding kinetics. Whilst all protocols can produce good solutions, diverse subunits always helps; these complexes access more efficient solutions when following external control protocols, and are simpler to design for internal control, as molecular interfaces do not need modification during assembly given sufficient variation in dimerization rates. Our results identify universal scaling in the cost of kinetic trapping, and provide multiple strategies for eliminating trapping and maximizing assembly yield across large parameter spaces.
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Affiliation(s)
| | | | - Yian Qian
- TC Jenkins Department of Biophysics, Johns Hopkins University, 3400 N Charles St, Baltimore, MD 21218
| | - Margaret E. Johnson
- TC Jenkins Department of Biophysics, Johns Hopkins University, 3400 N Charles St, Baltimore, MD 21218
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Qian Y, Evans D, Mishra B, Fu Y, Liu ZH, Guo S, Johnson ME. Temporal control by cofactors prevents kinetic trapping in retroviral Gag lattice assembly. Biophys J 2023; 122:3173-3190. [PMID: 37393432 PMCID: PMC10432227 DOI: 10.1016/j.bpj.2023.06.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2023] [Revised: 06/21/2023] [Accepted: 06/27/2023] [Indexed: 07/03/2023] Open
Abstract
For retroviruses like HIV to proliferate, they must form virions shaped by the self-assembly of Gag polyproteins into a rigid lattice. This immature Gag lattice has been structurally characterized and reconstituted in vitro, revealing the sensitivity of lattice assembly to multiple cofactors. Due to this sensitivity, the energetic criterion for forming stable lattices is unknown, as are their corresponding rates. Here, we use a reaction-diffusion model designed from the cryo-ET structure of the immature Gag lattice to map a phase diagram of assembly outcomes controlled by experimentally constrained rates and free energies, over experimentally relevant timescales. We find that productive assembly of complete lattices in bulk solution is extraordinarily difficult due to the large size of this ∼3700 monomer complex. Multiple Gag lattices nucleate before growth can complete, resulting in loss of free monomers and frequent kinetic trapping. We therefore derive a time-dependent protocol to titrate or "activate" the Gag monomers slowly within the solution volume, mimicking the biological roles of cofactors. This general strategy works remarkably well, yielding productive growth of self-assembled lattices for multiple interaction strengths and binding rates. By comparing to the in vitro assembly kinetics, we can estimate bounds on rates of Gag binding to Gag and the cellular cofactor IP6. Our results show that Gag binding to IP6 can provide the additional time delay necessary to support smooth growth of the immature lattice with relatively fast assembly kinetics, mostly avoiding kinetic traps. Our work provides a foundation for predicting and disrupting formation of the immature Gag lattice via targeting specific protein-protein binding interactions.
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Affiliation(s)
- Yian Qian
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland
| | - Daniel Evans
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland
| | - Bhavya Mishra
- Department of Physics, and Center for Cellular and Biomolecular Machines, University of California, Merced, California
| | - Yiben Fu
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland
| | - Zixiu Hugh Liu
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland
| | - Sikao Guo
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland
| | - Margaret E Johnson
- TC Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, Maryland.
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Volchek VV, Kompankov NB, Sokolov MN, Abramov PA. Proton Affinity in the Chemistry of Beta-Octamolybdate: HPLC-ICP-AES, NMR and Structural Studies. MOLECULES (BASEL, SWITZERLAND) 2022; 27:molecules27238368. [PMID: 36500457 PMCID: PMC9738851 DOI: 10.3390/molecules27238368] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/29/2022] [Revised: 11/23/2022] [Accepted: 11/25/2022] [Indexed: 12/05/2022]
Abstract
The affinity of [β-Mo8O26]4- toward different proton sources has been studied in various conditions. The proposed sites for proton coordination were highlighted with single crystal X-ray diffraction (SCXRD) analysis of (Bu4N)3[β-{Ag(py-NH2)Mo8O26]}] (1) and from analysis of reported structures. Structural rearrangement of [β-Mo8O26]4- as a direct response to protonation was studied in solution with 95Mo NMR and HPLC-ICP-AES techniques. A new type of proton transfer reaction between (Bu4N)4[β-Mo8O26] and (Bu4N)4H2[V10O28] in DMSO results in both polyoxometalates transformation into [V2Mo4O19]4-, which was confirmed by the 95Mo, 51V NMR and HPLC-ICP-AES techniques. The same type of reaction with [H4SiW12O40] in DMSO leads to metal redistribution with formation of [W2Mo4O19]2-.
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Affiliation(s)
- Victoria V. Volchek
- Nikolaev Institute of Inorganic Chemistry SB RAS, 3 Akad. Lavrentiev Ave., 630090 Novosibirsk, Russia
| | - Nikolay B. Kompankov
- Nikolaev Institute of Inorganic Chemistry SB RAS, 3 Akad. Lavrentiev Ave., 630090 Novosibirsk, Russia
| | - Maxim N. Sokolov
- Nikolaev Institute of Inorganic Chemistry SB RAS, 3 Akad. Lavrentiev Ave., 630090 Novosibirsk, Russia
| | - Pavel A. Abramov
- Nikolaev Institute of Inorganic Chemistry SB RAS, 3 Akad. Lavrentiev Ave., 630090 Novosibirsk, Russia
- Institute of Natural Sciences and Mathematics, Ural Federal University Named after B.N. Yeltsin, 620075 Ekaterinburg, Russia
- Correspondence:
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Becchi M, Capelli R, Perego C, Pavan GM, Micheletti C. Density-tunable pathway complexity in a minimalistic self-assembly model. SOFT MATTER 2022; 18:8106-8116. [PMID: 36239129 DOI: 10.1039/d2sm00968d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
An open challenge in self-assembly is learning how to design systems that can be conditionally guided towards different target structures depending on externally-controlled conditions. Using a theoretical and numerical approach, here we discuss a minimalistic self-assembly model that can be steered towards different types of ordered constructs at the equilibrium by solely tuning a facile selection parameter, namely the density of building blocks. Metadynamics and Langevin dynamics simulations allow us to explore the behavior of the system in and out of equilibrium conditions. We show that the density-driven tunability is encoded in the pathway complexity of the system, and specifically in the competition between two different main self-assembly routes. A comprehensive set of simulations provides insight into key factors allowing to make one self-assembling pathway prevailing on the other (or vice versa), determining the selection of the final self-assembled products. We formulate and validate a practical criterion for checking whether a specific molecular design is predisposed for such density-driven tunability of the products, thus offering a new, broader perspective to realize and harness this facile extrinsic control of conditional self-assembly.
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Affiliation(s)
- Matteo Becchi
- Scuola Internazionale Superiore di Studi Avanzati - SISSA, via Bonomea 265, 34136 Trieste, Italy.
| | - Riccardo Capelli
- Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
- Department of Biosciences, Università degli Studi di Milano, Via Giovanni Celoria 26, 20133 Milano, Italy
| | - Claudio Perego
- Department of Innovative Technologies, University of Applied Sciences and Arts of Southern Switzerland, Polo Universitario Lugano, Campus Est, Via la Santa 1, 6962 Lugano-Viganello, Switzerland
| | - Giovanni M Pavan
- Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
- Department of Innovative Technologies, University of Applied Sciences and Arts of Southern Switzerland, Polo Universitario Lugano, Campus Est, Via la Santa 1, 6962 Lugano-Viganello, Switzerland
| | - Cristian Micheletti
- Scuola Internazionale Superiore di Studi Avanzati - SISSA, via Bonomea 265, 34136 Trieste, Italy.
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