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Konevtsova OV, Chalin DV, Rochal SB. Theory of density waves and organization of proteins in icosahedral virus capsids. Phys Chem Chem Phys 2023; 26:569-580. [PMID: 38086647 DOI: 10.1039/d3cp05384a] [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: 12/22/2023]
Abstract
Understanding the physical principles underlying the structural organization of the proteinaceous viral shells is of major importance to advance antiviral strategies. Here, we develop a phenomenological thermodynamic theory, which considers structures of small and middle-size icosahedral viral shells as a result of condensation of a minimum number of protein density waves on a spherical surface. Each of these irreducible critical waves has icosahedral symmetry and can be expressed as a specific series of the spherical harmonics Ylm with the same wave number l. As we demonstrate, in small viral shells self-assembled from individual proteins, the maxima of one critical density wave determine the positions of proteins, while the spatial derivatives of the second one control the protein orientations on the shell surface. In contrast to the small shells, the middle-size ones are always formed from pentamers and hexamers (referred to as capsomers). Considering all such structures deposited in the Protein Data Bank, we unexpectedly found that the positions of capsomeres in these shells correspond to the maxima of interference patterns produced by no more than two critical waves with close wave numbers. This fact allows us to explain the observed limit size of the icosahedral shells assembled from pentamers and hexamers. We also construct nonequilibrium thermodynamic potentials describing the protein crystallization and discuss the reasons behind the specific handedness of the viral shells.
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Affiliation(s)
- Olga V Konevtsova
- Faculty of Physics, Southern Federal University, 5 Zorge str., 344090 Rostov-on-Don, Russia.
| | - Dmitrii V Chalin
- Faculty of Physics, Southern Federal University, 5 Zorge str., 344090 Rostov-on-Don, Russia.
| | - Sergei B Rochal
- Faculty of Physics, Southern Federal University, 5 Zorge str., 344090 Rostov-on-Don, Russia.
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Chalin D, Bureau C, Parmeggiani A, Rochal S, Kissa K, Golushko I. Modeling and live imaging of mechanical instabilities in the zebrafish aorta during hematopoiesis. Sci Rep 2021; 11:9316. [PMID: 33927284 PMCID: PMC8085226 DOI: 10.1038/s41598-021-88667-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Accepted: 04/01/2021] [Indexed: 01/27/2023] Open
Abstract
All blood cells originate from hematopoietic stem/progenitor cells (HSPCs). HSPCs are formed from endothelial cells (ECs) of the dorsal aorta (DA), via endothelial-to-hematopoietic transition (EHT). The zebrafish is a primary model organism to study the process in vivo. While the role of mechanical stress in controlling gene expression promoting cell differentiation is actively investigated, mechanisms driving shape changes of the DA and individual ECs remain poorly understood. We address this problem by developing a new DA micromechanical model and applying it to experimental data on zebrafish morphogenesis. The model considers the DA as an isotropic tubular membrane subjected to hydrostatic blood pressure and axial stress. The DA evolution is described as a movement in the dimensionless controlling parameters space: normalized hydrostatic pressure and axial stress. We argue that HSPC production is accompanied by two mechanical instabilities arising in the system due to the plane stress in the DA walls and show how a complex interplay between mechanical forces in the system drives the emerging morphological changes.
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Affiliation(s)
- Dmitrii Chalin
- Research and Education Center "Materials", Don State Technical University, 1 Gagarin Square, Rostov-on-Don, 344000, Russia
| | - Charlotte Bureau
- LPHI, University of Montpellier, CNRS, INSERM, Montpellier, France
| | - Andrea Parmeggiani
- LPHI, University of Montpellier, CNRS, INSERM, Montpellier, France.,Laboratoire Charles Coulomb, University of Montpellier, CNRS, Montpellier, France
| | - Sergei Rochal
- Faculty of Physics, Southern Federal University, Zorge 5, Rostov-on-Don, 344090, Russian Federation
| | - Karima Kissa
- LPHI, University of Montpellier, CNRS, INSERM, Montpellier, France.
| | - Ivan Golushko
- Research and Education Center "Materials", Don State Technical University, 1 Gagarin Square, Rostov-on-Don, 344000, Russia.
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Konevtsova OV, Roshal DS, Podgornik R, Rochal SB. Irreversible and reversible morphological changes in the φ6 capsid and similar viral shells: symmetry and micromechanics. SOFT MATTER 2020; 16:9383-9392. [PMID: 32945317 DOI: 10.1039/d0sm01338b] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Understanding the physicochemical processes occurring in viruses during their maturation is of fundamental importance since only mature viruses can infect host cells. Here we consider the irreversible and reversible morphological changes that occur with the dodecahedral φ6 procapsid during the sequential packaging of 3 RNA segments forming the viral genome. It is shown that the dodecahedral shape of all the four observed capsid states is perfectly reproduced by a sphere radially deformed by only two irreducible spherical harmonics with icosahedral symmetry and wave numbers l = 6 and l = 10. The rotation of proteins around the 3-fold axes at the Procapsid → Intermediate 1 irreversible transformation is in fact also well described with the shear field containing only two irreducible harmonics with the same two wave numbers. The high stability of the Intermediate 1 state is discussed and the shapes of the Intermediate 2 state and Capsid (reversibly transforming back to the Intermediate 1 state) are shown to be mainly due to the isotropic pressure that the encapsidated RNA segments exert on the shell walls. The hidden symmetry of the capsid and the physicochemical features of the in vitro genome extraction from the viral shell are also elucidated.
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Affiliation(s)
- Olga V Konevtsova
- Physics Faculty, Southern Federal University, Rostov-on-Don, Russia.
| | - Daria S Roshal
- Physics Faculty, Southern Federal University, Rostov-on-Don, Russia.
| | - Rudolf Podgornik
- Department of Theoretical Physics, JoŽef Stefan Institute, SI-1000 Ljubljana, Slovenia and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia and School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China and CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Sergei B Rochal
- Physics Faculty, Southern Federal University, Rostov-on-Don, Russia.
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Roshal D, Konevtsova O, Lošdorfer Božič A, Podgornik R, Rochal S. pH-induced morphological changes of proteinaceous viral shells. Sci Rep 2019; 9:5341. [PMID: 30926857 PMCID: PMC6440952 DOI: 10.1038/s41598-019-41799-6] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Accepted: 02/21/2019] [Indexed: 01/19/2023] Open
Abstract
Changes in environmental pH can induce morphological changes in empty proteinaceous shells of bacteriophages in vitro that are very similar to changes occurring in viral capsids in vivo after encapsidation of DNA. These changes in capsid shape and size cannot be explained with a simple elastic model alone. We propose a new theoretical framework that combines the elasticity of thin icosahedral shells with the pH dependence of capsid charge distribution. Minimization of the sum of elastic and electrostatic free energies leads to equilibrium shapes of viral shells that depend on a single elastic parameter and the detailed configuration of the imbedded protein charges. Based on the in vitro shell reconstructions of bacteriophage HK97 we elucidate the details of how the reversible transition between Prohead II and Expansion Intermediate II states of the HK97 procapsid is induced by pH changes, as well as some other features of the bacteriophage maturation.
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Affiliation(s)
- D Roshal
- Physics Faculty, Southern Federal University, Rostov-on-Don, Russia
| | - O Konevtsova
- Physics Faculty, Southern Federal University, Rostov-on-Don, Russia
| | - A Lošdorfer Božič
- Department of Theoretical Physics, Jožef Stefan Institute, SI-1000, Ljubljana, Slovenia
| | - R Podgornik
- Department of Theoretical Physics, Jožef Stefan Institute, SI-1000, Ljubljana, Slovenia.
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000, Ljubljana, Slovenia.
- School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China.
- CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
| | - S Rochal
- Physics Faculty, Southern Federal University, Rostov-on-Don, Russia
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Rochal SB, Konevtsova OV, Lorman VL. Static and dynamic hidden symmetries of icosahedral viral capsids. NANOSCALE 2017; 9:12449-12460. [PMID: 28809986 DOI: 10.1039/c7nr04020b] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Viral shells self-assemble from identical proteins, which tend to form equivalent environments in the resulting assembly. However, in icosahedral capsids containing more than 60 proteins, they are enforced to occupy not only the symmetrically equivalent locations but also the quasi-equivalent ones. Due to this important fact, static and dynamic symmetries of viral shells can include additional hidden components. Here, developing the Caspar and Klug ideas concerning the quasi-equivalence of protein environments, we derive the simplest hexagonal tilings, that in principle could correspond to the local protein order in viral shells, and apply the resulting theory to nucleocytoplasmic large dsDNA viruses. In addition, analyzing the dynamic symmetry of the P22 viral shell, we demonstrate that the collective critical modes responsible for the protein reorganization during the procapsid maturation are approximately equivalent to the normal modes of the isotropic spherical membrane with O(3) symmetry. Furthermore, we establish the relationship between the dynamic symmetry of the P22 procapsid and the protein arrangement regularities that appear only in the mature capsid.
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Affiliation(s)
- Sergey B Rochal
- Faculty of Physics, Southern Federal University, 5 Zorge str., 344090 Rostov-on-Don, Russia.
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Roshal DS, Konevtsova OV, Myasnikova AE, Rochal SB. Assembly of the most topologically regular two-dimensional micro and nanocrystals with spherical, conical, and tubular shapes. Phys Rev E 2016; 94:052605. [PMID: 27967001 DOI: 10.1103/physreve.94.052605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Indexed: 06/06/2023]
Abstract
We consider how to control the extension of curvature-induced defects in the hexagonal order covering different curved surfaces. In these frames we propose a physical mechanism for improving structures of two-dimensional spherical colloidal crystals (SCCs). For any SCC comprising of about 300 or less particles the mechanism transforms all extended topological defects (ETDs) in the hexagonal order into the point disclinations. Perfecting the structure is carried out by successive cycles of the particle implantation and subsequent relaxation of the crystal. The mechanism is potentially suitable for obtaining colloidosomes with better selective permeability. Our approach enables modeling the most topologically regular tubular and conical two-dimensional nanocrystals including various possible polymorphic forms of the HIV viral capsid. Different HIV-like shells with an arbitrary number of structural units (SUs) and desired geometrical parameters are easily formed. Faceting of the obtained structures is performed by minimizing the suggested elastic energy.
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Affiliation(s)
- D S Roshal
- Faculty of Physics, Southern Federal University, 5 Zorge strasse, 344090 Rostov-on-Don, Russia
| | - O V Konevtsova
- Faculty of Physics, Southern Federal University, 5 Zorge strasse, 344090 Rostov-on-Don, Russia
| | - A E Myasnikova
- Faculty of Physics, Southern Federal University, 5 Zorge strasse, 344090 Rostov-on-Don, Russia
| | - S B Rochal
- Faculty of Physics, Southern Federal University, 5 Zorge strasse, 344090 Rostov-on-Don, Russia
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