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Gandikota MC, Das S, Cacciuto A. Spontaneous crumpling of active spherical shells. SOFT MATTER 2024; 20:3635-3640. [PMID: 38619604 DOI: 10.1039/d4sm00015c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/16/2024]
Abstract
The existence of a crumpled phase for self-avoiding elastic surfaces was postulated more than three decades ago using simple Flory-like scaling arguments. Despite much effort, its stability in a microscopic environment has been the subject of much debate. In this paper we show how a crumpled phase develops reliably and consistently upon subjecting a thin spherical shell to active fluctuations. We find a master curve describing how the relative volume of a shell changes with the strength of the active forces, that applies for every shell independent of size and elastic constants. Furthermore, we extract a general expression for the onset active force beyond which a shell begins to crumple. Finally, we calculate how the size exponent varies along the crumpling curve.
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Affiliation(s)
- M C Gandikota
- Department of Chemistry, Columbia University, 3000 Broadway, NY 10027, New York, USA.
| | - Shibananda Das
- Department of Chemistry, Columbia University, 3000 Broadway, NY 10027, New York, USA.
- Institute for Theoretical Physics, Georg-August University, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - A Cacciuto
- Department of Chemistry, Columbia University, 3000 Broadway, NY 10027, New York, 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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Liu Y, Lee TU, Rezaee Javan A, Xie YM. Extending Goldberg's method to parametrize and control the geometry of Goldberg polyhedra. ROYAL SOCIETY OPEN SCIENCE 2022; 9:220675. [PMID: 35958093 PMCID: PMC9363989 DOI: 10.1098/rsos.220675] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/21/2022] [Accepted: 07/15/2022] [Indexed: 06/15/2023]
Abstract
Goldberg polyhedra have been widely studied across multiple fields, as their distinctive pattern can lead to many useful applications. Their topology can be determined using Goldberg's method through generating topologically equivalent structures, named cages. However, the geometry of Goldberg polyhedra remains underexplored. This study extends Goldberg's framework to a new method that can systematically determine the topology and effectively control the geometry of Goldberg polyhedra based on the initial shapes of cages. In detail, we first parametrize the cage's geometry under specified topology and polyhedral symmetry; then, we manipulate the predefined independent variables through optimization to achieve the user-defined geometric properties. The benchmark problem of finding equilateral Goldberg polyhedra is solved to demonstrate the effectiveness of the proposed method. Using this method, we have successfully achieved nearly exact spherical Goldberg polyhedra, with all vertices on a sphere and all faces being planar under extremely low numerical errors. Such results serve as strong numerical evidence for the existence of this new type of Goldberg polyhedra. Furthermore, we iteratively perform k-means clustering and optimization to significantly reduce the number of different edge lengths to benefit the cost reduction for architectural and engineering applications.
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Affiliation(s)
- Yuanpeng Liu
- Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne 3001, Australia
| | - Ting-Uei Lee
- Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne 3001, Australia
| | - Anooshe Rezaee Javan
- Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne 3001, Australia
| | - Yi Min Xie
- Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne 3001, Australia
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Božič A, Šiber A. Mechanics of inactive swelling and bursting of porate pollen grains. Biophys J 2022; 121:782-792. [PMID: 35093340 PMCID: PMC8943692 DOI: 10.1016/j.bpj.2022.01.019] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Revised: 11/23/2021] [Accepted: 01/21/2022] [Indexed: 11/02/2022] Open
Abstract
The structure of pollen grains, which is typically characterized by soft apertures in an otherwise stiff exine shell, guides their response to changes in the humidity of the environment. These changes can lead to desiccation of the grain and its infolding but also to excessive swelling of the grain and even its bursting. Here we use an elastic model to explore the mechanics of pollen grain swelling and the role of soft, circular apertures (pores) in this process. Small, circular apertures typically occur in airborne and allergenic pollen grains so that the bursting of such grains is important in the context of human health. We identify and quantify a mechanical weakness of the pores, which are prone to rapid inflation when the grain swells to a critical extent. The inflation occurs as a sudden transition and may induce bursting of the grain and release of its content. This process crucially depends on the size of the pores and their softness. Our results provide insight into the inactive part of the mechanical response of pollen grains to hydration when they land on a stigma as well as bursting of airborne pollen grains during changes in air humidity.
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Affiliation(s)
- Anže Božič
- Department of Theoretical Physics, Jožef Stefan Institute, Ljubljana, Slovenia
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Martín-Bravo M, Llorente JMG, Hernández-Rojas J, Wales DJ. Minimal Design Principles for Icosahedral Virus Capsids. ACS NANO 2021; 15:14873-14884. [PMID: 34492194 PMCID: PMC8939845 DOI: 10.1021/acsnano.1c04952] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2021] [Indexed: 06/13/2023]
Abstract
The geometrical structures of single- and multiple-shell icosahedral virus capsids are reproduced as the targets that minimize the cost corresponding to relatively simple design functions. Capsid subunits are first identified as building blocks at a given coarse-grained scale and then represented in these functions as point particles located on an appropriate number of concentric spherical surfaces. Minimal design cost is assigned to optimal spherical packings of the particles. The cost functions are inspired by the packings favored for the Thomson problem, which minimize the electrostatic potential energy between identical charged particles. In some cases, icosahedral symmetry constraints are incorporated as external fields acting on the particles. The simplest cost functions can be obtained by separating particles in disjoint nonequivalent sets with distinct interactions, or by introducing interacting holes (the absence of particles). These functions can be adapted to reproduce any capsid structure found in real viruses. Structures absent in Nature require significantly more complex designs. Measures of information content and complexity are assigned to both the cost functions and the capsid geometries. In terms of these measures, icosahedral structures and the corresponding cost functions are the simplest solutions.
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Affiliation(s)
- Manuel Martín-Bravo
- Departamento
de Física and IUdEA, Universidad
de La Laguna, 38205 Tenerife, Spain
| | | | | | - David J. Wales
- Department
of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United
Kingdom
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Javidpour L, BoŽič A, Naji A, Podgornik R. Electrostatic interactions between the SARS-CoV-2 virus and a charged electret fibre. SOFT MATTER 2021; 17:4296-4303. [PMID: 33908595 DOI: 10.1039/d1sm00232e] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
While almost any kind of face mask offers some protection against particles and pathogens of different sizes, the most efficient ones make use of a layered structure where one or more layers are electrically charged. These electret layers are essential for the efficient filtration of difficult-to-capture small particles, yet the exact nature of electrostatic capture with respect to the charge on both the particles and the electret fibres as well as the effect of the immediate environment remain unclear. Here, we explore in detail the electrostatic interactions between the surface of a single charged electret fibre and a model of the SARS-CoV-2 virus. Using Poisson-Boltzmann electrostatics coupled to a detailed spike protein charge regulation model, we show how pH and salt concentration drastically change both the scale and the sign of the interaction. Furthermore, the configuration of the few spike proteins closest to the electret fibre turns out to be as important for the strength of the interaction as their total number on the virus envelope, a direct consequence of spike protein charge regulation. The results of our work elucidate the details of virus electrostatics and contribute to the general understanding of efficient virus filtration mechanisms.
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Affiliation(s)
- Leili Javidpour
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5531, Iran
| | - AnŽe BoŽič
- Department of Theoretical Physics, JoŽef Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - Ali Naji
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5531, Iran and School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5531, Iran
| | - Rudolf Podgornik
- School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. and Wenzhou Institute of the University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
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Emanuel MD, Cherstvy AG, Metzler R, Gompper G. Buckling transitions and soft-phase invasion of two-component icosahedral shells. Phys Rev E 2021; 102:062104. [PMID: 33465945 DOI: 10.1103/physreve.102.062104] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2020] [Accepted: 11/11/2020] [Indexed: 12/18/2022]
Abstract
What is the optimal distribution of two types of crystalline phases on the surface of icosahedral shells, such as of many viral capsids? We here investigate the distribution of a thin layer of soft material on a crystalline convex icosahedral shell. We demonstrate how the shapes of spherical viruses can be understood from the perspective of elasticity theory of thin two-component shells. We develop a theory of shape transformations of an icosahedral shell upon addition of a softer, but still crystalline, material onto its surface. We show how the soft component "invades" the regions with the highest elastic energy and stress imposed by the 12 topological defects on the surface. We explore the phase diagram as a function of the surface fraction of the soft material, the shell size, and the incommensurability of the elastic moduli of the rigid and soft phases. We find that, as expected, progressive filling of the rigid shell by the soft phase starts from the most deformed regions of the icosahedron. With a progressively increasing soft-phase coverage, the spherical segments of domes are filled first (12 vertices of the shell), then the cylindrical segments connecting the domes (30 edges) are invaded, and, ultimately, the 20 flat faces of the icosahedral shell tend to be occupied by the soft material. We present a detailed theoretical investigation of the first two stages of this invasion process and develop a model of morphological changes of the cone structure that permits noncircular cross sections. In conclusion, we discuss the biological relevance of some structures predicted from our calculations, in particular for the shape of viral capsids.
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Affiliation(s)
- Marc D Emanuel
- Theoretical Physics of Living Matter, Institute of Biological Information Processing, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany.,Kavli Institute for Nanoscience, Technical University Delft, 2628 CJ Delft, Netherlands
| | - Andrey G Cherstvy
- Theoretical Physics of Living Matter, Institute of Biological Information Processing, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany.,Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Gerhard Gompper
- Theoretical Physics of Living Matter, Institute of Biological Information Processing, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
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