1
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Clark AB, Safdari M, Zoorob S, Zandi R, van der Schoot P. Relaxational dynamics of the T-number conversion of virus capsids. J Chem Phys 2023; 159:084904. [PMID: 37610017 DOI: 10.1063/5.0160822] [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: 06/05/2023] [Accepted: 08/07/2023] [Indexed: 08/24/2023] Open
Abstract
We extend a recently proposed kinetic theory of virus capsid assembly based on Model A kinetics and study the dynamics of the interconversion of virus capsids of different sizes triggered by a quench, that is, by sudden changes in the solution conditions. The work is inspired by in vitro experiments on functionalized coat proteins of the plant virus cowpea chlorotic mottle virus, which undergo a reversible transition between two different shell sizes (T = 1 and T = 3) upon changing the acidity and salinity of the solution. We find that the relaxation dynamics are governed by two time scales that, in almost all cases, can be identified as two distinct processes. Initially, the monomers and one of the two types of capsids respond to the quench. Subsequently, the monomer concentration remains essentially constant, and the conversion between the two capsid species completes. In the intermediate stages, a long-lived metastable steady state may present itself, where the thermodynamically less stable species predominate. We conclude that a Model A based relaxational model can reasonably describe the early and intermediate stages of the conversion experiments. However, it fails to provide a good representation of the time evolution of the state of assembly of the coat proteins in the very late stages of equilibration when one of the two species disappears from the solution. It appears that explicitly incorporating the nucleation barriers to assembly and disassembly is crucial for an accurate description of the experimental findings, at least under conditions where these barriers are sufficiently large.
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Affiliation(s)
- Alexander Bryan Clark
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Mohammadamin Safdari
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Selim Zoorob
- Biophysics Graduate Program, University of California, Riverside, California 92521, USA
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
- Biophysics Graduate Program, University of California, Riverside, California 92521, USA
| | - Paul van der Schoot
- Department of Applied Physics and Science Education, Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, The Netherlands
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2
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Brackley CA, Lips A, Morozov A, Poon WCK, Marenduzzo D. Mechanisms for destabilisation of RNA viruses at air-water and liquid-liquid interfaces. Nat Commun 2021; 12:6812. [PMID: 34819516 PMCID: PMC8613244 DOI: 10.1038/s41467-021-27052-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 10/22/2021] [Indexed: 11/19/2022] Open
Abstract
Understanding the interactions between viruses and surfaces or interfaces is important, as they provide the principles underpinning the cleaning and disinfection of contaminated surfaces. Yet, the physics of such interactions is currently poorly understood. For instance, there are longstanding experimental observations suggesting that the presence of air-water interfaces can generically inactivate and kill viruses, yet the mechanism underlying this phenomenon remains unknown. Here we use theory and simulations to show that electrostatics may provide one such mechanism, and that this is very general. Thus, we predict that the electrostatic free energy of an RNA virus should increase by several thousands of kBT as the virion breaches an air-water interface. We also show that the fate of a virus approaching a generic liquid-liquid interface depends strongly on the detailed balance between interfacial and electrostatic forces, which can be tuned, for instance, by choosing different media to contact a virus-laden respiratory droplet. Tunability arises because both the electrostatic and interfacial forces scale similarly with viral size. We propose that these results can be used to design effective strategies for surface disinfection. We know that air-water interfaces can generically inactivate viruses, but the mechanisms behind this observation are unclear. Here the authors use simulations to uncover those mechanisms and find that the electrostatic repulsive free energy of an RNA virus increases by several thousands of kBT as it approaches an air-water interface, providing a mechanism for viral destabilization which may induce inactivation.
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Affiliation(s)
- C A Brackley
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, Scotland, UK
| | - A Lips
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, Scotland, UK
| | - A Morozov
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, Scotland, UK
| | - W C K Poon
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, Scotland, UK
| | - D Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, Scotland, UK.
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3
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Marichal L, Gargowitsch L, Rubim RL, Sizun C, Kra K, Bressanelli S, Dong Y, Panahandeh S, Zandi R, Tresset G. Relationships between RNA topology and nucleocapsid structure in a model icosahedral virus. Biophys J 2021; 120:3925-3936. [PMID: 34418368 PMCID: PMC8511167 DOI: 10.1016/j.bpj.2021.08.021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Revised: 06/21/2021] [Accepted: 08/13/2021] [Indexed: 10/20/2022] Open
Abstract
The process of genome packaging in most of viruses is poorly understood, notably the role of the genome itself in the nucleocapsid structure. For simple icosahedral single-stranded RNA viruses, the branched topology due to the RNA secondary structure is thought to lower the free energy required to complete a virion. We investigate the structure of nucleocapsids packaging RNA segments with various degrees of compactness by small-angle x-ray scattering and cryotransmission electron microscopy. The structural differences are mild even though compact RNA segments lead on average to better-ordered and more uniform particles across the sample. Numerical calculations confirm that the free energy is lowered for the RNA segments displaying the larger number of branch points. The effect is, however, opposite with synthetic polyelectrolytes, in which a star topology gives rise to more disorder in the capsids than a linear topology. If RNA compactness and size account in part for the proper assembly of the nucleocapsid and the genome selectivity, other factors most likely related to the host cell environment during viral assembly must come into play as well.
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Affiliation(s)
- Laurent Marichal
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay, France
| | - Laetitia Gargowitsch
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay, France
| | - Rafael Leite Rubim
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay, France
| | - Christina Sizun
- Université Paris-Saclay, CNRS, Institut de Chimie des Substances Naturelles, Gif-sur-Yvette, France
| | - Kalouna Kra
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay, France; Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell, Gif-sur-Yvette, France
| | - Stéphane Bressanelli
- Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell, Gif-sur-Yvette, France
| | - Yinan Dong
- Department of Physics and Astronomy, University of California, Riverside, California
| | - Sanaz Panahandeh
- Department of Physics and Astronomy, University of California, Riverside, California
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, California
| | - Guillaume Tresset
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay, France.
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4
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Hill SR, Twarock R, Dykeman EC. The impact of local assembly rules on RNA packaging in a T = 1 satellite plant virus. PLoS Comput Biol 2021; 17:e1009306. [PMID: 34428224 PMCID: PMC8384211 DOI: 10.1371/journal.pcbi.1009306] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 07/26/2021] [Indexed: 02/05/2023] Open
Abstract
The vast majority of viruses consist of a nucleic acid surrounded by a protective icosahedral protein shell called the capsid. During viral infection of a host cell, the timing and efficiency of the assembly process is important for ensuring the production of infectious new progeny virus particles. In the class of single-stranded RNA (ssRNA) viruses, the assembly of the capsid takes place in tandem with packaging of the ssRNA genome in a highly cooperative co-assembly process. In simple ssRNA viruses such as the bacteriophage MS2 and small RNA plant viruses such as STNV, this cooperative process results from multiple interactions between the protein shell and sites in the RNA genome which have been termed packaging signals. Using a stochastic assembly algorithm which includes cooperative interactions between the protein shell and packaging signals in the RNA genome, we demonstrate that highly efficient assembly of STNV capsids arises from a set of simple local rules. Altering the local assembly rules results in different nucleation scenarios with varying assembly efficiencies, which in some cases depend strongly on interactions with RNA packaging signals. Our results provide a potential simple explanation based on local assembly rules for the ability of some ssRNA viruses to spontaneously assemble around charged polymers and other non-viral RNAs in vitro.
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Affiliation(s)
- Sam R. Hill
- Department of Mathematics, University of York, York, United Kingdom
- York Cross-Disciplinary Centre for Systems Analysis, University of York, York, United Kingdom
| | - Reidun Twarock
- Department of Mathematics, University of York, York, United Kingdom
- Department of Biology, University of York, York, United Kingdom
- York Cross-Disciplinary Centre for Systems Analysis, University of York, York, United Kingdom
| | - Eric C. Dykeman
- Department of Mathematics, University of York, York, United Kingdom
- York Cross-Disciplinary Centre for Systems Analysis, University of York, York, United Kingdom
- * E-mail:
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5
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Abstract
Much of virus fate, both in the environment and in physical/chemical treatment, is dependent on electrostatic interactions. Developing an accurate means of predicting virion isoelectric point (pI) would help to understand and anticipate virus fate and transport, especially for viruses that are not readily propagated in the lab. One simple approach to predicting pI estimates the pH at which the sum of charges from ionizable amino acids in capsid proteins approaches zero. However, predicted pIs based on capsid charges frequently deviate by several pH units from empirically measured pIs. Recently, the discrepancy between empirical and predicted pI was attributed to the electrostatic neutralization of predictable polynucleotide-binding regions (PBRs) of the capsid interior. In this paper, we review models presupposing (i) the influence of the viral polynucleotide on surface charge or (ii) the contribution of only exterior residues to surface charge. We then compare these models to the approach of excluding only PBRs and hypothesize a conceptual electrostatic model that aligns with this approach. The PBR exclusion method outperformed methods based on three-dimensional (3D) structure and accounted for major discrepancies in predicted pIs without adversely affecting pI prediction for a diverse range of viruses. In addition, the PBR exclusion method was determined to be the best available method for predicting virus pI, since (i) PBRs are predicted independently of the impact on pI, (ii) PBR prediction relies on proteome sequences rather than detailed structural models, and (iii) PBR exclusion was successfully demonstrated on a diverse set of viruses. These models apply to nonenveloped viruses only. A similar model for enveloped viruses is complicated by a lack of data on enveloped virus pI, as well as uncertainties regarding the influence of the phospholipid envelope on charge and ion gradients.
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Affiliation(s)
- Joe Heffron
- Department of Civil, Construction and Environmental Engineering, Marquette University, Milwaukee, Wisconsin, USA
| | - Brooke K Mayer
- Department of Civil, Construction and Environmental Engineering, Marquette University, Milwaukee, Wisconsin, USA
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6
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Dong Y, Li S, Zandi R. Effect of the charge distribution of virus coat proteins on the length of packaged RNAs. Phys Rev E 2020; 102:062423. [PMID: 33466113 DOI: 10.1103/physreve.102.062423] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2020] [Accepted: 11/17/2020] [Indexed: 01/20/2023]
Abstract
Single-stranded RNA viruses efficiently encapsulate their genome into a protein shell called the capsid. Electrostatic interactions between the positive charges in the capsid protein's N-terminal tail and the negatively charged genome have been postulated as the main driving force for virus assembly. Recent experimental results indicate that the N-terminal tail with the same number of charges and same lengths packages different amounts of RNA, which reveals that electrostatics alone cannot explain all the observed outcomes of the RNA self-assembly experiments. Using a mean-field theory, we show that the combined effect of genome configurational entropy and electrostatics can explain to some extent the amount of packaged RNA with mutant proteins where the location and number of charges on the tails are altered. Understanding the factors contributing to the virus assembly could promote the attempt to block viral infections or to build capsids for gene therapy applications.
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Affiliation(s)
- Yinan Dong
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Siyu Li
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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7
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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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8
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Viruses with different genome types adopt a similar strategy to pack nucleic acids based on positively charged protein domains. Sci Rep 2020; 10:5470. [PMID: 32214181 PMCID: PMC7096446 DOI: 10.1038/s41598-020-62328-w] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Accepted: 03/02/2020] [Indexed: 11/17/2022] Open
Abstract
Capsid proteins often present a positively charged arginine-rich sequence at their terminal regions, which has a fundamental role in genome packaging and particle stability for some icosahedral viruses. These sequences show little to no conservation and are structurally dynamic such that they cannot be easily detected by common sequence or structure comparisons. As a result, the occurrence and distribution of positively charged domains across the viral universe are unknown. Based on the net charge calculation of discrete protein segments, we identified proteins containing amino acid stretches with a notably high net charge (Q > + 17), which are enriched in icosahedral viruses with a distinctive bias towards arginine over lysine. We used viral particle structural data to calculate the total electrostatic charge derived from the most positively charged protein segment of capsid proteins and correlated these values with genome charges arising from the phosphates of each nucleotide. We obtained a positive correlation (r = 0.91, p-value <0001) for a group of 17 viral families, corresponding to 40% of all families with icosahedral structures described to date. These data indicated that unrelated viruses with diverse genome types adopt a common underlying mechanism for capsid assembly based on R-arms.
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9
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Panahandeh S, Li S, Marichal L, Leite Rubim R, Tresset G, Zandi R. How a Virus Circumvents Energy Barriers to Form Symmetric Shells. ACS NANO 2020; 14:3170-3180. [PMID: 32115940 DOI: 10.1021/acsnano.9b08354] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Previous self-assembly experiments on a model icosahedral plant virus have shown that, under physiological conditions, capsid proteins initially bind to the genome through an en masse mechanism and form nucleoprotein complexes in a disordered state, which raises the question as to how virions are assembled into a highly ordered structure in the host cell. Using small-angle X-ray scattering, we find out that a disorder-order transition occurs under physiological conditions upon an increase in capsid protein concentrations. Our cryo-transmission electron microscopy reveals closed spherical shells containing in vitro transcribed viral RNA even at pH 7.5, in marked contrast with the previous observations. We use Monte Carlo simulations to explain this disorder-order transition and find that, as the shell grows, the structures of disordered intermediates in which the distribution of pentamers does not belong to the icosahedral subgroups become energetically so unfavorable that the caps can easily dissociate and reassemble, overcoming the energy barriers for the formation of perfect icosahedral shells. In addition, we monitor the growth of capsids under the condition that the nucleation and growth is the dominant pathway and show that the key for the disorder-order transition in both en masse and nucleation and growth pathways lies in the strength of elastic energy compared to the other forces in the system including protein-protein interactions and the chemical potential of free subunits. Our findings explain, at least in part, why perfect virions with icosahedral order form under different conditions including physiological ones.
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Affiliation(s)
- Sanaz Panahandeh
- Department of Physics and Astronomy, University of California, Riverside, California 92521, United States
| | - Siyu Li
- Department of Physics and Astronomy, University of California, Riverside, California 92521, United States
| | - Laurent Marichal
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Rafael Leite Rubim
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Guillaume Tresset
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, United States
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10
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Sun X, Li D, Wang Z, Liu Q, Wei Y, Liu T. A dimorphism shift of hepatitis B virus capsids in response to ionic conditions. NANOSCALE 2018; 10:16984-16989. [PMID: 30183040 DOI: 10.1039/c8nr03370f] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The dimorphism of HBV capsids (coexistence of T = 3 and T = 4 capsids) was found to be regulatable by controlling the rate of capsid nucleation using cations such as K+ or Ca2+: a quick addition of highly concentrated monovalent and/or multivalent counter-cations resulted in a morphism transition from a thermodynamically more stable, T = 4 capsid-dominant state (>80% of total capsids) to a new state containing ∼1 : 1 amounts of T = 3 and T = 4 capsids. These results suggested that the salts with strong charge screening ability could narrow the difference in nucleation energy barriers between the two states, which were not inter-convertible once formed. The effect of salts was more significant than other factors such as pH or protein concentration in achieving such a dimorphism shift. The general mechanism of HBV capsid dimorphism described here provides a new perspective in understanding the virus assembly during infection and directing the design of non-infectious capsids for nanotechnology applications.
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Affiliation(s)
- Xinyu Sun
- Department of Polymer Science, University of Akron, Akron, Ohio, USA.
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11
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Lošdorfer Božič A, Šiber A. Electrostatics-Driven Inflation of Elastic Icosahedral Shells as a Model for Swelling of Viruses. Biophys J 2018; 115:822-829. [PMID: 30139522 DOI: 10.1016/j.bpj.2018.07.032] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2018] [Revised: 07/20/2018] [Accepted: 07/30/2018] [Indexed: 01/13/2023] Open
Abstract
We develop a clear theoretical description of radial swelling in virus-like particles that delineates the importance of electrostatic contributions to swelling in the absence of any conformational changes. The model couples the elastic parameters of the capsid-represented as a continuous elastic shell-to the electrostatic pressure acting on it. We show that different modifications of the electrostatic interactions brought about by, for instance, changes in pH or solution ionic strength are often sufficient to achieve the experimentally observed swelling (∼10% of the capsid radius). Additionally, we derive analytical expressions for the electrostatics-driven radial swelling of virus-like particles that enable one to quickly estimate the magnitudes of physical quantities involved.
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12
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Systematic analysis of biological roles of charged amino acid residues located throughout the structured inner wall of a virus capsid. Sci Rep 2018; 8:9543. [PMID: 29934575 PMCID: PMC6015035 DOI: 10.1038/s41598-018-27749-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Accepted: 06/01/2018] [Indexed: 12/31/2022] Open
Abstract
Structure-based mutational analysis of viruses is providing many insights into the relationship between structure and biological function of macromolecular complexes. We have systematically investigated the individual biological roles of charged residues located throughout the structured capsid inner wall (outside disordered peptide segments) of a model spherical virus, the minute virus of mice (MVM). The functional effects of point mutations that altered the electrical charge at 16 different positions at the capsid inner wall were analyzed. The results revealed that MVM capsid self-assembly is rather tolerant to point mutations that alter the number and distribution of charged residues at the capsid inner wall. However, mutations that either increased or decreased the number of positive charges around capsid-bound DNA segments reduced the thermal resistance of the virion. Moreover, mutations that either removed or changed the positions of negatively charged carboxylates in rings of acidic residues around capsid pores were deleterious by precluding a capsid conformational transition associated to through-pore translocation events. The results suggest that number, distribution and specific position of electrically charged residues across the inner wall of a spherical virus may have been selected through evolution as a compromise between several different biological requirements.
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13
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Shojaei HR, Muthukumar M. Adsorption and encapsulation of flexible polyelectrolytes in charged spherical vesicles. J Chem Phys 2018; 146:244901. [PMID: 28668020 DOI: 10.1063/1.4986961] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a theory of adsorption of flexible polyelectrolytes on the interior and exterior surfaces of a charged vesicle in an electrolyte solution. The criteria for adsorption and the density profiles of the adsorbed polymer chain are derived in terms of various characteristics of the polymer, vesicle, and medium, such as the charge density and length of the polymer, charge density and size of the vesicle, electrolyte concentration and dielectric constant of the medium. For adsorption inside the vesicle, the competition between the loss of conformational entropy and gain in adsorption energy results in two kinds of encapsulated states, depending on the strength of the polymer-vesicle interaction. By considering also the adsorption from outside the vesicle, we derive the entropic and energy contributions to the free energy change to transfer an adsorbed chain in the interior to an adsorbed chain on the exterior. In this paper, we have used the Wentzel-Kramers-Brillouin (WKB) method to solve the equation for the probability distribution function of the chain. The present WKB results are compared with the previous results based on variational methods. The WKB and variational results are in good agreement for both the interior and exterior states of adsorption, except in the zero-salt limit for adsorption in the exterior region. The adsorption criteria and density profiles for both the interior and exterior states are presented in terms of various experimentally controllable variables. Calculation of the dependencies of free energy change to transfer an adsorbed chain from the interior to the exterior surface on salt concentration and vesicle radius shows that the free energy penalty to expel a chain from a vesicle is only of the order of thermal energy.
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Affiliation(s)
- H R Shojaei
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - M Muthukumar
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
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14
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Li S, Orland H, Zandi R. Self consistent field theory of virus assembly. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:144002. [PMID: 29460850 PMCID: PMC7104907 DOI: 10.1088/1361-648x/aab0c6] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2017] [Revised: 02/12/2018] [Accepted: 02/20/2018] [Indexed: 05/04/2023]
Abstract
The ground state dominance approximation (GSDA) has been extensively used to study the assembly of viral shells. In this work we employ the self-consistent field theory (SCFT) to investigate the adsorption of RNA onto positively charged spherical viral shells and examine the conditions when GSDA does not apply and SCFT has to be used to obtain a reliable solution. We find that there are two regimes in which GSDA does work. First, when the genomic RNA length is long enough compared to the capsid radius, and second, when the interaction between the genome and capsid is so strong that the genome is basically localized next to the wall. We find that for the case in which RNA is more or less distributed uniformly in the shell, regardless of the length of RNA, GSDA is not a good approximation. We observe that as the polymer-shell interaction becomes stronger, the energy gap between the ground state and first excited state increases and thus GSDA becomes a better approximation. We also present our results corresponding to the genome persistence length obtained through the tangent-tangent correlation length and show that it is zero in case of GSDA but is equal to the inverse of the energy gap when using SCFT.
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Affiliation(s)
- Siyu Li
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, United States of America
- Institut de Physique Théorique, CEA-Saclay, CEA, F-91191 Gif-sur-Yvette, France
- Beijing Computational Science Research Center, No.10 East Xibeiwang Road, Haidan District, Beijing 100193, People’s Republic of China
| | - Henri Orland
- Institut de Physique Théorique, CEA-Saclay, CEA, F-91191 Gif-sur-Yvette, France
- Beijing Computational Science Research Center, No.10 East Xibeiwang Road, Haidan District, Beijing 100193, People’s Republic of China
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, United States of America
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15
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van der Holst B, Kegel WK, Zandi R, van der Schoot P. The different faces of mass action in virus assembly. J Biol Phys 2018; 44:163-179. [PMID: 29616429 PMCID: PMC5928020 DOI: 10.1007/s10867-018-9487-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Accepted: 03/16/2018] [Indexed: 02/06/2023] Open
Abstract
The spontaneous encapsulation of genomic and non-genomic polyanions by coat proteins of simple icosahedral viruses is driven, in the first instance, by electrostatic interactions with polycationic RNA binding domains on these proteins. The efficiency with which the polyanions can be encapsulated in vitro, and presumably also in vivo, must in addition be governed by the loss of translational and mixing entropy associated with co-assembly, at least if this co-assembly constitutes a reversible process. These forms of entropy counteract the impact of attractive interactions between the constituents and hence they counteract complexation. By invoking mass action-type arguments and a simple model describing electrostatic interactions, we show how these forms of entropy might settle the competition between negatively charged polymers of different molecular weights for co-assembly with the coat proteins. In direct competition, mass action turns out to strongly work against the encapsulation of RNAs that are significantly shorter, which is typically the case for non-viral (host) RNAs. We also find that coat proteins favor forming virus particles over nonspecific binding to other proteins in the cytosol even if these are present in vast excess. Our results rationalize a number of recent in vitro co-assembly experiments showing that short polyanions are less effective at attracting virus coat proteins to form virus-like particles than long ones do, even if both are present at equal weight concentrations in the assembly mixture.
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Affiliation(s)
- Bart van der Holst
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Willem K Kegel
- Department of Chemistry, Utrecht University, Utrecht, The Netherlands
| | - Roya Zandi
- Department of Physics and Astronomy, University of California Riverside, Riverside, USA
| | - Paul van der Schoot
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands. .,Institute for Theoretical Physics, Utrecht University, Utrecht, The Netherlands.
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16
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Li S, Erdemci-Tandogan G, van der Schoot P, Zandi R. The effect of RNA stiffness on the self-assembly of virus particles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:044002. [PMID: 29235442 PMCID: PMC7104906 DOI: 10.1088/1361-648x/aaa159] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2017] [Revised: 12/06/2017] [Accepted: 12/13/2017] [Indexed: 05/21/2023]
Abstract
Under many in vitro conditions, some small viruses spontaneously encapsidate a single stranded (ss) RNA into a protein shell called the capsid. While viral RNAs are found to be compact and highly branched because of long distance base-pairing between nucleotides, recent experiments reveal that in a head-to-head competition between an ssRNA with no secondary or higher order structure and a viral RNA, the capsid proteins preferentially encapsulate the linear polymer! In this paper, we study the impact of genome stiffness on the encapsidation free energy of the complex of RNA and capsid proteins. We show that an increase in effective chain stiffness because of base-pairing could be the reason why under certain conditions linear chains have an advantage over branched chains when it comes to encapsidation efficiency. While branching makes the genome more compact, RNA base-pairing increases the effective Kuhn length of the RNA molecule, which could result in an increase of the free energy of RNA confinement, that is, the work required to encapsidate RNA, and thus less efficient packaging.
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Affiliation(s)
- Siyu Li
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, United States of America
| | - Gonca Erdemci-Tandogan
- Department of Physics, Syracuse University, Syracuse, NY 13244, United States of America
| | - Paul van der Schoot
- Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, Netherlands
- Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, United States of America
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17
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Lošdorfer Božič A, Podgornik R. Varieties of charge distributions in coat proteins of ssRNA+ viruses. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:024001. [PMID: 29182522 PMCID: PMC7104810 DOI: 10.1088/1361-648x/aa9ded] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/21/2017] [Revised: 11/21/2017] [Accepted: 11/28/2017] [Indexed: 06/07/2023]
Abstract
A major part of the interactions involved in the assembly and stability of icosahedral, positive-sense single-stranded RNA (ssRNA+) viruses is electrostatic in nature, as can be inferred from the strong pH- and salt-dependence of their assembly phase diagrams. Electrostatic interactions do not act only between the capsid coat proteins (CPs), but just as often provide a significant contribution to the interactions of the CPs with the genomic RNA, mediated to a large extent by positively charged, flexible N-terminal tails of the CPs. In this work, we provide two clear and complementary definitions of an N-terminal tail of a protein, and use them to extract the tail sequences of a large number of CPs of ssRNA+ viruses. We examine the pH-dependent interplay of charge on both tails and CPs alike, and show that-in contrast to the charge on the CPs-the net positive charge on the N-tails persists even to very basic pH values. In addition, we note a limit to the length of the wild-type genomes of those viruses which utilize positively charged tails, when compared to viruses without charged tails and similar capsid size. At the same time, we observe no clear connection between the charge on the N-tails and the genome lengths of the viruses included in our study.
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Affiliation(s)
- Anže Lošdorfer Božič
- Department of Theoretical Physics, Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia
| | - Rudolf 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
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18
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Muthukumar M. 50th Anniversary Perspective: A Perspective on Polyelectrolyte Solutions. Macromolecules 2017; 50:9528-9560. [PMID: 29296029 PMCID: PMC5746850 DOI: 10.1021/acs.macromol.7b01929] [Citation(s) in RCA: 259] [Impact Index Per Article: 37.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2017] [Revised: 11/27/2017] [Indexed: 12/17/2022]
Abstract
From the beginning of life with the information-containing polymers until the present era of a plethora of water-based materials in health care industry and biotechnology, polyelectrolytes are ubiquitous with a broad range of structural and functional properties. The main attribute of polyelectrolyte solutions is that all molecules are strongly correlated both topologically and electrostatically in their neutralizing background of charged ions in highly polarizable solvent. These strong correlations and the necessary use of numerous variables in experiments on polyelectrolytes have presented immense challenges toward fundamental understanding of the various behaviors of charged polymeric systems. This Perspective presents the author's subjective summary of several conceptual advances and the remaining persistent challenges in the contexts of charge and size of polymers, structures in homogeneous solutions, thermodynamic instability and phase transitions, structural evolution with oppositely charged polymers, dynamics in polyelectrolyte solutions, kinetics of phase separation, mobility of charged macromolecules between compartments, and implications to biological systems.
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Affiliation(s)
- M. Muthukumar
- Department of Polymer Science
and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, United States
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19
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Erdemci-Tandogan G, Orland H, Zandi R. RNA Base Pairing Determines the Conformations of RNA Inside Spherical Viruses. PHYSICAL REVIEW LETTERS 2017; 119:188102. [PMID: 29219580 DOI: 10.1103/physrevlett.119.188102] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2017] [Indexed: 05/21/2023]
Abstract
Many simple RNA viruses enclose their genetic material by a protein shell called the capsid. While the capsid structures are well characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it remain poorly understood. We study the impact of base pairing on the conformations of RNA and find that it undergoes a swollen coil to globule continuous transition as a function of the strength of the pairing interaction. We also observe a first order transition and kink profile as a function of RNA length. All these transitions could explain the different RNA profiles observed inside viral shells.
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Affiliation(s)
- Gonca Erdemci-Tandogan
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Henri Orland
- Institut de Physique Théorique, CEA-Saclay, CEA, F-91191 Gif-sur-Yvette, France
- Beijing Computational Science Research Center, No. 10 East Xibeiwang Road, Haidan District, Beijing 100193, China
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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20
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Li S, Erdemci-Tandogan G, Wagner J, van der Schoot P, Zandi R. Impact of a nonuniform charge distribution on virus assembly. Phys Rev E 2017; 96:022401. [PMID: 28950450 DOI: 10.1103/physreve.96.022401] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2017] [Indexed: 01/04/2023]
Abstract
Many spherical viruses encapsulate their genomes in protein shells with icosahedral symmetry. This process is spontaneous and driven by electrostatic interactions between positive domains on the virus coat proteins and the negative genomes. We model the effect of the nonuniform icosahedral charge distribution from the protein shell instead using a mean-field theory. We find that this nonuniform charge distribution strongly affects the optimal genome length and that it can explain the experimentally observed phenomenon of overcharging of virus and viruslike particles.
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Affiliation(s)
- Siyu Li
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Gonca Erdemci-Tandogan
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Jef Wagner
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Paul van der Schoot
- Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.,Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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21
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Li C, Kneller AR, Jacobson SC, Zlotnick A. Single Particle Observation of SV40 VP1 Polyanion-Induced Assembly Shows That Substrate Size and Structure Modulate Capsid Geometry. ACS Chem Biol 2017; 12:1327-1334. [PMID: 28323402 DOI: 10.1021/acschembio.6b01066] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Simian virus 40 capsid protein (VP1) is a unique system for studying substrate-dependent assembly of a nanoparticle. Here, we investigate a simplest case of this system where 12 VP1 pentamers and a single polyanion, e.g., RNA, form a T = 1 particle. To test the roles of polyanion substrate length and structure during assembly, we characterized the assembly products with size exclusion chromatography, transmission electron microscopy, and single-particle resistive-pulse sensing. We found that 500 and 600 nt RNAs had the optimal length and structure for assembly of uniform T = 1 particles. Longer 800 nt RNA, shorter 300 nt RNA, and a linear 600 unit poly(styrene sulfonate) (PSS) polyelectrolyte produced heterogeneous populations of products. This result was surprising as the 600mer PSS and 500-600 nt RNA have similar mass and charge. Like ssRNA, PSS also has a short 4 nm persistence length, but unlike RNA, PSS lacks a compact tertiary structure. These data indicate that even for flexible substrates, shape as well as size affect assembly and are consistent with the hypothesis that work, derived from protein-protein and protein-substrate interactions, is used to compact the substrate.
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Affiliation(s)
- Chenglei Li
- Department
of Molecular and Cellular Biochemistry and ‡Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Andrew R. Kneller
- Department
of Molecular and Cellular Biochemistry and ‡Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Stephen C. Jacobson
- Department
of Molecular and Cellular Biochemistry and ‡Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Adam Zlotnick
- Department
of Molecular and Cellular Biochemistry and ‡Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
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22
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Angelescu DG. Assembled viral-like nanoparticles from elastic capsomers and polyion. J Chem Phys 2017; 146:134902. [DOI: 10.1063/1.4979496] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
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23
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Erdemci-Tandogan G, Wagner J, van der Schoot P, Podgornik R, Zandi R. Effects of RNA branching on the electrostatic stabilization of viruses. Phys Rev E 2016; 94:022408. [PMID: 27627336 DOI: 10.1103/physreve.94.022408] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Indexed: 11/07/2022]
Abstract
Many single-stranded (ss) ribonucleic acid (RNA) viruses self-assemble from capsid protein subunits and the nucleic acid to form an infectious virion. It is believed that the electrostatic interactions between the negatively charged RNA and the positively charged viral capsid proteins drive the encapsidation, although there is growing evidence that the sequence of the viral RNA also plays a role in packaging. In particular, the sequence will determine the possible secondary structures that the ssRNA will take in solution. In this work, we use a mean-field theory to investigate how the secondary structure of the RNA combined with electrostatic interactions affects the efficiency of assembly and stability of the assembled virions. We show that the secondary structure of RNA may result in negative osmotic pressures while a linear polymer causes positive osmotic pressures for the same conditions. This may suggest that the branched structure makes the RNA more effectively packaged and the virion more stable.
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Affiliation(s)
- Gonca Erdemci-Tandogan
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Jef Wagner
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Paul van der Schoot
- Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands.,Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
| | - Rudolf Podgornik
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.,Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia.,Department of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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24
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Kim J, Wu J. A Thermodynamic Model for Genome Packaging in Hepatitis B Virus. Biophys J 2016; 109:1689-97. [PMID: 26488660 DOI: 10.1016/j.bpj.2015.08.021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2015] [Revised: 08/02/2015] [Accepted: 08/10/2015] [Indexed: 12/12/2022] Open
Abstract
Understanding the fundamentals of genome packaging in viral capsids is important for finding effective antiviral strategies and for utilizing benign viral particles for gene therapy. While the structure of encapsidated genomic materials has been routinely characterized with experimental techniques such as cryo-electron microscopy and x-ray diffraction, much less is known about the molecular driving forces underlying genome assembly in an intracellular environment and its in vivo interactions with the capsid proteins. Here we study the thermodynamic basis of the pregenomic RNA encapsidation in human Hepatitis B virus in vivo using a coarse-grained molecular model that captures the essential components of nonspecific intermolecular interactions. The thermodynamic model is used to examine how the electrostatic interaction between the packaged RNA and the highly charged C-terminal domains (CTD) of capsid proteins regulate the nucleocapsid formation. The theoretical model predicts optimal RNA content in Hepatitis B virus nucleocapsids with different CTD lengths in good agreement with mutagenesis measurements, confirming the predominant role of electrostatic interactions and molecular excluded-volume effects in genome packaging. We find that the amount of encapsidated RNA is not linearly correlated with the net charge of CTD tails as suggested by earlier theoretical studies. Our thermodynamic analysis of the nucleocapsid structure and stability indicates that ∼10% of the CTD residues are free from complexation with RNA, resulting in partially exposed CTD tails. The thermodynamic model also predicts the free energy of complex formation between macromolecules, which corroborates experimental results for the impact of CTD truncation on the nucleocapsid stability.
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Affiliation(s)
- Jehoon Kim
- Department of Chemical and Environmental Engineering, University of California at Riverside, Riverside, California
| | - Jianzhong Wu
- Department of Chemical and Environmental Engineering, University of California at Riverside, Riverside, California.
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25
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Smith GR, Xie L, Schwartz R. Modeling Effects of RNA on Capsid Assembly Pathways via Coarse-Grained Stochastic Simulation. PLoS One 2016; 11:e0156547. [PMID: 27244559 PMCID: PMC4887116 DOI: 10.1371/journal.pone.0156547] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2015] [Accepted: 05/16/2016] [Indexed: 12/02/2022] Open
Abstract
The environment of a living cell is vastly different from that of an in vitro reaction system, an issue that presents great challenges to the use of in vitro models, or computer simulations based on them, for understanding biochemistry in vivo. Virus capsids make an excellent model system for such questions because they typically have few distinct components, making them amenable to in vitro and modeling studies, yet their assembly can involve complex networks of possible reactions that cannot be resolved in detail by any current experimental technology. We previously fit kinetic simulation parameters to bulk in vitro assembly data to yield a close match between simulated and real data, and then used the simulations to study features of assembly that cannot be monitored experimentally. The present work seeks to project how assembly in these simulations fit to in vitro data would be altered by computationally adding features of the cellular environment to the system, specifically the presence of nucleic acid about which many capsids assemble. The major challenge of such work is computational: simulating fine-scale assembly pathways on the scale and in the parameter domains of real viruses is far too computationally costly to allow for explicit models of nucleic acid interaction. We bypass that limitation by applying analytical models of nucleic acid effects to adjust kinetic rate parameters learned from in vitro data to see how these adjustments, singly or in combination, might affect fine-scale assembly progress. The resulting simulations exhibit surprising behavioral complexity, with distinct effects often acting synergistically to drive efficient assembly and alter pathways relative to the in vitro model. The work demonstrates how computer simulations can help us understand how assembly might differ between the in vitro and in vivo environments and what features of the cellular environment account for these differences.
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Affiliation(s)
- Gregory R. Smith
- Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
| | - Lu Xie
- Joint Carnegie Mellon/University of Pittsburgh Ph.D. Program in Computational Biology, Pittsburgh, Pennsylvania, United States of America
- Computational Biology Department, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
| | - Russell Schwartz
- Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- Computational Biology Department, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
- * E-mail:
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26
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Erdemci-Tandogan G, Wagner J, van der Schoot P, Zandi R. Role of Genome in the Formation of Conical Retroviral Shells. J Phys Chem B 2016; 120:6298-305. [PMID: 27128962 DOI: 10.1021/acs.jpcb.6b02712] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Human immunodeficiency virus (HIV) capsid proteins spontaneously assemble around the genome into a protective protein shell called the capsid, which can take on a variety of shapes broadly classified as conical, cylindrical, and irregular. The majority of capsids seen in in vivo studies are conical in shape, while in vitro experiments have shown a preference for cylindrical capsids. The factors involved in the selection of the unique shape of HIV capsids are not well understood, and in particular the impact of RNA on the formation of the capsid is not known. In this work, we study the role of the genome and its interaction with the capsid protein by modeling the genomic RNA through a mean-field theory. Our results show that the confinement free energy for a homopolymeric model genome confined in a conical capsid is lower than that in a cylindrical capsid, at least when the genome does not interact with the capsid, which seems to be the case in in vivo experiments. Conversely, the confinement free energy for the cylinder is lower than that for a conical capsid if the genome is attracted to the capsid proteins as the in vitro experiments. Understanding the factors that contribute to the formation of conical capsids may shed light on the infectivity of HIV particles.
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Affiliation(s)
- Gonca Erdemci-Tandogan
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - Jef Wagner
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - Paul van der Schoot
- Group Theory of Polymers and Soft Matter, Eindhoven University of Technology , P.O. Box 513, 5600 MB Eindhoven, The Netherlands.,Institute for Theoretical Physics, Utrecht University , Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
| | - Roya Zandi
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
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27
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Wagner J, Erdemci-Tandogan G, Zandi R. Adsorption of annealed branched polymers on curved surfaces. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:495101. [PMID: 26574170 DOI: 10.1088/0953-8984/27/49/495101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
The behavior of annealed branched polymers near adsorbing surfaces plays a fundamental role in many biological and industrial processes. Most importantly single stranded RNA in solution tends to fold up and self-bind to form a highly branched structure. Using a mean field theory, we both perturbatively and numerically examine the adsorption of branched polymers on surfaces of several different geometries in a good solvent. Independent of the geometry of the wall, we observe that as branching density increases, surface tension decreases. However, we find a coupling between the branching density and curvature in that a further lowering of surface tension occurs when the wall curves towards the polymer, but the amount of lowering of surface tension decreases when the wall curves away from the polymer. We find that for branched polymers confined into spherical cavities, most of branch-points are located in the vicinity of the interior wall and the surface tension is minimized for a critical cavity radius. For branch polymers next to sinusoidal surfaces, we find that branch-points accumulate at the valleys while end-points on the peaks.
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Affiliation(s)
- Jef Wagner
- Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
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28
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Mamasakhlisov YS, Bellucci S, Hayryan S, Caturyan H, Grigoryan Z, Hu CK. Collapse and hybridization of RNA: view from replica technique approach. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:100. [PMID: 26385736 DOI: 10.1140/epje/i2015-15100-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2015] [Revised: 07/19/2015] [Accepted: 07/31/2015] [Indexed: 06/05/2023]
Abstract
The replica technique method is applied to investigate the kinetic behavior of the coarse-grained model for the RNA molecule. A non-equilibrium phase transition of second order between the glassy phase and the ensemble of freely fluctuating structures has been observed. The non-equilibrium steady state is investigated as well and the thermodynamic characteristics of the system have been evaluated. The non-equilibrium behavior of the specific heat is discussed. Based on our analysis, we point out the state in the kinetic pathway in which the RNA molecule is most prone to hybridization.
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Affiliation(s)
| | - S Bellucci
- INFN-Laboratori Nazionali di Frascati, Via Enrico Fermi, 40, 00044, Frascati RM, Italy
| | - Shura Hayryan
- Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., 11529, Nankang, Taipei, Taiwan
| | - H Caturyan
- Yerevan State University, 1 A. Manoogian Str., 0025, Yerevan, Armenia
| | - Z Grigoryan
- Goris State University, 4 Avangard Str., 3204, Goris, Armenia
| | - Chin-Kun Hu
- Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., 11529, Nankang, Taipei, Taiwan.
- National Center for Theoretical Sciences, National Tsing Hua University, 30013, Hsinchu, Taiwan.
- Business School, University of Shanghai for Science and Technology, 200093, Shanghai, China.
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29
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Grigoryan ZA, Karapetian AT. The Globular State of the Single-Stranded RNA: Effect of the Secondary Structure Rearrangements. J Nucleic Acids 2015; 2015:295264. [PMID: 26345143 PMCID: PMC4546806 DOI: 10.1155/2015/295264] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2015] [Revised: 07/06/2015] [Accepted: 07/06/2015] [Indexed: 11/26/2022] Open
Abstract
The mutual influence of the slow rearrangements of secondary structure and fast collapse of the long single-stranded RNA (ssRNA) in approximation of coarse-grained model is studied with analytic calculations. It is assumed that the characteristic time of the secondary structure rearrangement is much longer than that for the formation of the tertiary structure. A nonequilibrium phase transition of the 2nd order has been observed.
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Affiliation(s)
| | - Armen T. Karapetian
- Yerevan State University of Architecture and Construction, Teryan 105, 0009 Yerevan, Armenia
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30
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de Carvalho SJ, Metzler R, Cherstvy AG. Inverted critical adsorption of polyelectrolytes in confinement. SOFT MATTER 2015; 11:4430-4443. [PMID: 25940939 DOI: 10.1039/c5sm00635j] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density σc-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of σc for the concave interfaces versus the Debye screening length 1/κ and the extent of confinement a for these three interfaces for small κa values. For large κa the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/κ. We also rationalize how σc(κ) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.
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Affiliation(s)
- Sidney J de Carvalho
- Institute of Biosciences, Letters and Exact Sciences, Sao Paulo State University, 15054-000 Sao Jose do Rio Preto, Brazil.
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31
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Kim J, Wu J. A molecular thermodynamic model for the stability of hepatitis B capsids. J Chem Phys 2015; 140:235101. [PMID: 24952568 DOI: 10.1063/1.4882068] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Self-assembly of capsid proteins and genome encapsidation are two critical steps in the life cycle of most plant and animal viruses. A theoretical description of such processes from a physiochemical perspective may help better understand viral replication and morphogenesis thus provide fresh insights into the experimental studies of antiviral strategies. In this work, we propose a molecular thermodynamic model for predicting the stability of Hepatitis B virus (HBV) capsids either with or without loading nucleic materials. With the key components represented by coarse-grained thermodynamic models, the theoretical predictions are in excellent agreement with experimental data for the formation free energies of empty T4 capsids over a broad range of temperature and ion concentrations. The theoretical model predicts T3/T4 dimorphism also in good agreement with the capsid formation at in vivo and in vitro conditions. In addition, we have studied the stability of the viral particles in response to physiological cellular conditions with the explicit consideration of the hydrophobic association of capsid subunits, electrostatic interactions, molecular excluded volume effects, entropy of mixing, and conformational changes of the biomolecular species. The course-grained model captures the essential features of the HBV nucleocapsid stability revealed by recent experiments.
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Affiliation(s)
- Jehoon Kim
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, USA
| | - Jianzhong Wu
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, USA
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32
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Pujos JS, Maggs AC. Convexity and Stiffness in Energy Functions for Electrostatic Simulations. J Chem Theory Comput 2015; 11:1419-27. [PMID: 26574353 DOI: 10.1021/acs.jctc.5b00023] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We study the properties of convex functionals which have been proposed for the simulation of charged molecular systems within the Poisson-Boltzmann approximation. We consider the extent to which the functionals reproduce the true fluctuations of electrolytes and thus the one-loop correction to mean field theory-including the Debye-Hückel correction to the free energy of ionic solutions. We also compare the functionals for use in numerical optimization of a mean field model of a charged polymer and show that different functionals have very different stiffnesses leading to substantial differences in accuracy and speed.
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Affiliation(s)
- Justine S Pujos
- Laboratoire PCT, Gulliver CNRS-ESPCI UMR 7083 , 10 rue Vauquelin, 75231 Paris Cedex 05, France
| | - A C Maggs
- Laboratoire PCT, Gulliver CNRS-ESPCI UMR 7083 , 10 rue Vauquelin, 75231 Paris Cedex 05, France
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33
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Abstract
Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell called a capsid and in some cases are surrounded by a lipid bilayer membrane. This review summarizes the physics that govern the processes by which capsids assemble within their host cells and in vitro. We describe the thermodynamics and kinetics for the assembly of protein subunits into icosahedral capsid shells and how these are modified in cases in which the capsid assembles around a nucleic acid or on a lipid bilayer. We present experimental and theoretical techniques used to characterize capsid assembly, and we highlight aspects of virus assembly that are likely to receive significant attention in the near future.
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Affiliation(s)
- Jason D Perlmutter
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454;
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34
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Abstract
I present a review of the theoretical and computational methodologies that have been used to model the assembly of viral capsids. I discuss the capabilities and limitations of approaches ranging from equilibrium continuum theories to molecular dynamics simulations, and I give an overview of some of the important conclusions about virus assembly that have resulted from these modeling efforts. Topics include the assembly of empty viral shells, assembly around single-stranded nucleic acids to form viral particles, and assembly around synthetic polymers or charged nanoparticles for nanotechnology or biomedical applications. I present some examples in which modeling efforts have promoted experimental breakthroughs, as well as directions in which the connection between modeling and experiment can be strengthened.
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35
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Perlmutter JD, Perkett MR, Hagan MF. Pathways for virus assembly around nucleic acids. J Mol Biol 2014; 426:3148-3165. [PMID: 25036288 DOI: 10.1016/j.jmb.2014.07.004] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2014] [Revised: 06/17/2014] [Accepted: 07/07/2014] [Indexed: 12/25/2022]
Abstract
Understanding the pathways by which viral capsid proteins assemble around their genomes could identify key intermediates as potential drug targets. In this work, we use computer simulations to characterize assembly over a wide range of capsid protein-protein interaction strengths and solution ionic strengths. We find that assembly pathways can be categorized into two classes, in which intermediates are either predominantly ordered or disordered. Our results suggest that estimating the protein-protein and the protein-genome binding affinities may be sufficient to predict which pathway occurs. Furthermore, the calculated phase diagrams suggest that knowledge of the dominant assembly pathway and its relationship to control parameters could identify optimal strategies to thwart or redirect assembly to block infection. Finally, analysis of simulation trajectories suggests that the two classes of assembly pathways can be distinguished in single-molecule fluorescence correlation spectroscopy or bulk time-resolved small-angle X-ray scattering experiments.
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Affiliation(s)
- Jason D Perlmutter
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02454, USA
| | - Matthew R Perkett
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02454, USA
| | - Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02454, USA.
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36
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Javidpour L, Losdorfer Bozic A, Naji A, Podgornik R. Multivalent ion effects on electrostatic stability of virus-like nano-shells. J Chem Phys 2014; 139:154709. [PMID: 24160535 DOI: 10.1063/1.4825099] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Electrostatic properties and stability of charged virus-like nano-shells are examined in ionic solutions with monovalent and multivalent ions. A theoretical model based on a thin charged spherical shell and multivalent ions within the "dressed multivalent ion" approximation, yielding their distribution across the shell and the corresponding electrostatic (osmotic) pressure acting on the shell, is compared with extensive implicit Monte-Carlo simulations. It is found to be accurate for positive or low negative surface charge densities of the shell and for sufficiently high (low) monovalent (multivalent) salt concentrations. Phase diagrams involving electrostatic pressure exhibit positive and negative values, corresponding to an outward and an inward facing force on the shell, respectively. This provides an explanation for the high sensitivity of viral shell stability and self-assembly of viral capsid shells on the ionic environment.
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Affiliation(s)
- Leili Javidpour
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
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37
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Erdemci-Tandogan G, Wagner J, van der Schoot P, Podgornik R, Zandi R. RNA topology remolds electrostatic stabilization of viruses. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032707. [PMID: 24730874 DOI: 10.1103/physreve.89.032707] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2013] [Indexed: 06/03/2023]
Abstract
Simple RNA viruses efficiently encapsulate their genome into a nano-sized protein shell: the capsid. Spontaneous coassembly of the genome and the capsid proteins is driven predominantly by electrostatic interactions between the negatively charged RNA and the positively charged inner capsid wall. Using field theoretic formulation we show that the inherently branched RNA secondary structure allows viruses to maximize the amount of encapsulated genome and make assembly more efficient, allowing viral RNAs to out-compete cellular RNAs during replication in infected host cells.
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Affiliation(s)
- Gonca Erdemci-Tandogan
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Jef Wagner
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Paul van der Schoot
- Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
| | - Rudolf Podgornik
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia and Department of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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38
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Polles G, Indelicato G, Potestio R, Cermelli P, Twarock R, Micheletti C. Mechanical and assembly units of viral capsids identified via quasi-rigid domain decomposition. PLoS Comput Biol 2013; 9:e1003331. [PMID: 24244139 PMCID: PMC3828136 DOI: 10.1371/journal.pcbi.1003331] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2013] [Accepted: 09/13/2013] [Indexed: 02/05/2023] Open
Abstract
Key steps in a viral life-cycle, such as self-assembly of a protective protein container or in some cases also subsequent maturation events, are governed by the interplay of physico-chemical mechanisms involving various spatial and temporal scales. These salient aspects of a viral life cycle are hence well described and rationalised from a mesoscopic perspective. Accordingly, various experimental and computational efforts have been directed towards identifying the fundamental building blocks that are instrumental for the mechanical response, or constitute the assembly units, of a few specific viral shells. Motivated by these earlier studies we introduce and apply a general and efficient computational scheme for identifying the stable domains of a given viral capsid. The method is based on elastic network models and quasi-rigid domain decomposition. It is first applied to a heterogeneous set of well-characterized viruses (CCMV, MS2, STNV, STMV) for which the known mechanical or assembly domains are correctly identified. The validated method is next applied to other viral particles such as L-A, Pariacoto and polyoma viruses, whose fundamental functional domains are still unknown or debated and for which we formulate verifiable predictions. The numerical code implementing the domain decomposition strategy is made freely available. The genetic material of viruses is packaged inside capsids constituted from a few tens to thousands of proteins. The latter can organize in multimers that serve as fundamental blocks for the viral shell assembly or that control the capsid conformational transitions and response to mechanical stress. In this work, we introduce and apply a computational scheme that identifies the fundamental protein blocks from the structural fluctuations of the capsids in thermal equilibrium. These can be derived from phenomenological elastic network models with minimal computational expenditure. Accordingly, the basic functional protein units of a capsid can be obtained from the sole input of the capsid crystal structure. The method is applied to a heterogeneous set of viruses of various size and geometries. These include well-characterised instances for validation purposes, as well as debated ones for which predictions are formulated.
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Affiliation(s)
- Guido Polles
- International School for Advanced Studies (SISSA), Trieste, Italy
| | - Giuliana Indelicato
- York Centre for Complex Systems Analysis, Department of Mathematics, University of York, York, United Kingdom
| | | | - Paolo Cermelli
- Dipartimento di Matematica, Università di Torino, Torino, Italy
| | - Reidun Twarock
- York Centre for Complex Systems Analysis, Department of Mathematics, University of York, York, United Kingdom
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39
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Zhang R, Linse P. Icosahedral capsid formation by capsomers and short polyions. J Chem Phys 2013; 138:154901. [PMID: 23614442 DOI: 10.1063/1.4799243] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Kinetical and structural aspects of the capsomer-polyion co-assembly into icosahedral viruses have been simulated by molecular dynamics using a coarse-grained model comprising cationic capsomers and short anionic polyions. Conditions were found at which the presence of polyions of a minimum length was necessary for capsomer formation. The largest yield of correctly formed capsids was obtained at which the driving force for capsid formation was relatively weak. Relatively stronger driving forces, i.e., stronger capsomer-capsomer short-range attraction and∕or stronger electrostatic interaction, lead to larger fraction of kinetically trapped structures and aberrant capsids. The intermediate formation was investigated and different evolving scenarios were found by just varying the polyion length.
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Affiliation(s)
- Ran Zhang
- Physical Chemistry, Department of Chemistry, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden.
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40
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He L, Porterfield Z, van der Schoot P, Zlotnick A, Dragnea B. Hepatitis virus capsid polymorph stability depends on encapsulated cargo size. ACS NANO 2013; 7:8447-54. [PMID: 24010404 PMCID: PMC5683388 DOI: 10.1021/nn4017839] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
Protein cages providing a controlled environment to encapsulated cargo are a ubiquitous presence in any biological system. Well-known examples are capsids, the regular protein shells of viruses, which protect and deliver the viral genome. Since some virus capsids can be loaded with nongenomic cargoes, they are interesting for a variety of applications ranging from biomedical delivery to energy harvesting. A question of vital importance for such applications is how does capsid stability depend on the size of the cargo? A nanoparticle-templated assembly approach was employed here to determine how different polymorphs of the Hepatitis B virus icosahedral capsid respond to a gradual change in the encapsulated cargo size. It was found that assembly into complete virus-like particles occurs cooperatively around a variety of core diameters, albeit the degree of cooperativity varies. Among these virus-like particles, it was found that those of an outer diameter corresponding to an icosahedral array of 240 proteins (T = 4) are able to accommodate the widest range of cargo sizes.
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Affiliation(s)
- Li He
- Department of Chemistry and ‡Department of Molecular and Cellular Biochemistry, Indiana University , Bloomington, Indiana 47405, United States
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41
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Perlmutter JD, Qiao C, Hagan MF. Viral genome structures are optimal for capsid assembly. eLife 2013; 2:e00632. [PMID: 23795290 PMCID: PMC3683802 DOI: 10.7554/elife.00632] [Citation(s) in RCA: 96] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2013] [Accepted: 05/14/2013] [Indexed: 12/21/2022] Open
Abstract
Understanding how virus capsids assemble around their nucleic acid (NA) genomes could promote efforts to block viral propagation or to reengineer capsids for gene therapy applications. We develop a coarse-grained model of capsid proteins and NAs with which we investigate assembly dynamics and thermodynamics. In contrast to recent theoretical models, we find that capsids spontaneously ‘overcharge’; that is, the negative charge of the NA exceeds the positive charge on capsid. When applied to specific viruses, the optimal NA lengths closely correspond to the natural genome lengths. Calculations based on linear polyelectrolytes rather than base-paired NAs underpredict the optimal length, demonstrating the importance of NA structure to capsid assembly. These results suggest that electrostatics, excluded volume, and NA tertiary structure are sufficient to predict assembly thermodynamics and that the ability of viruses to selectively encapsidate their genomic NAs can be explained, at least in part, on a thermodynamic basis. DOI:http://dx.doi.org/10.7554/eLife.00632.001 Viruses are infectious agents made up of proteins and a genome made of DNA or RNA. Upon infecting a host cell, viruses hijack the cell’s gene expression machinery and force it to produce copies of the viral genome and proteins, which then assemble into new viruses that can eventually infect other host cells. Because assembly is an essential step in the viral life cycle, understanding how this process occurs could significantly advance the fight against viral diseases. In many viral families, a protein shell called a capsid forms around the viral genome during the assembly process. However, capsids can also assemble around nucleic acids in solution, indicating that a host cell is not required for their formation. Since capsid proteins are positively charged, and nucleic acids are negatively charged, electrostatic interactions between the two are thought to have an important role in capsid assembly. However, it is unclear how structural features of the viral genome affect assembly, and why the negative charge on viral genomes is actually far greater than the positive charge on capsids. These questions are difficult to address experimentally because most of the intermediates that form during virus assembly are too short-lived to be imaged. Here, Perlmutter et al. have used state of the art computational methods and advances in graphical processing units (GPUs) to produce the most realistic model of capsid assembly to date. They showed that the stability of the complex formed between the nucleic acid and the capsid depends on the length of the viral genome. Yield was highest for genomes within a certain range of lengths, and capsids that assembled around longer or shorter genomes tended to be malformed. Perlmutter et al. also explored how structural features of the virus—including base-pairing between viral nucleic acids, and the size and charge of the capsid—determine the optimal length of the viral genome. When they included structural data from real viruses in their simulations and predicted the optimal lengths for the viral genome, the results were very similar to those seen in existing viruses. This indicates that the structure of the viral genome has been optimized to promote packaging into capsids. Understanding this relationship between structure and packaging will make it easier to develop antiviral agents that thwart or misdirect virus assembly, and could aid the redesign of viruses for use in gene therapy and drug delivery. DOI:http://dx.doi.org/10.7554/eLife.00632.002
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Affiliation(s)
- Jason D Perlmutter
- Martin A Fisher School of Physics , Brandeis University , Waltham , United States
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42
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van der Schoot P, Zandi R. Impact of the topology of viral RNAs on their encapsulation by virus coat proteins. J Biol Phys 2013; 39:289-99. [PMID: 23860874 DOI: 10.1007/s10867-013-9307-y] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2013] [Accepted: 02/07/2013] [Indexed: 11/28/2022] Open
Abstract
Single-stranded RNAs of simple viruses seem to be topologically more compact than other types of single-stranded RNA. It has been suggested that this has an evolutionary purpose: more compact structures are more easily encapsulated in the limited space that the cavity of the virus capsid offers. We employ a simple Flory theory to calculate the optimal amount of polymers confined in a viral shell. We find that the free energy gain or more specifically the efficiency of RNA encapsidation increases substantially with topological compactness. We also find that the optimal length of RNA encapsidated in a capsid increases with the degree of branching of the genome even though this effect is very weak. Further, we show that if the structure of the branching of the polymer is allowed to anneal, the optimal loading increases substantially.
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Affiliation(s)
- Paul van der Schoot
- Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands
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43
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Saper G, Kler S, Asor R, Oppenheim A, Raviv U, Harries D. Effect of capsid confinement on the chromatin organization of the SV40 minichromosome. Nucleic Acids Res 2013; 41:1569-80. [PMID: 23258701 PMCID: PMC3561987 DOI: 10.1093/nar/gks1270] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2012] [Revised: 10/26/2012] [Accepted: 11/05/2012] [Indexed: 01/10/2023] Open
Abstract
Using small-angle X-ray scattering, we determined the three-dimensional packing architecture of the minichromosome confined within the SV40 virus. In solution, the minichromosome, composed of closed circular dsDNA complexed in nucleosomes, was shown to be structurally similar to cellular chromatin. In contrast, we find a unique organization of the nanometrically encapsidated chromatin, whereby minichromosomal density is somewhat higher at the center of the capsid and decreases towards the walls. This organization is in excellent agreement with a coarse-grained computer model, accounting for tethered nucleosomal interactions under viral capsid confinement. With analogy to confined liquid crystals, but contrary to the solenoid structure of cellular chromatin, our simulations indicate that the nucleosomes within the capsid lack orientational order. Nucleosomes in the layer adjacent to the capsid wall, however, align with the boundary, thereby inducing a 'molten droplet' state of the chromatin. These findings indicate that nucleosomal interactions suffice to predict the genome organization in polyomavirus capsids and underscore the adaptable nature of the eukaryotic chromatin architecture to nanoscale confinement.
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Affiliation(s)
- Gadiel Saper
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel, The Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel and Department of Hematology, Hebrew University–Hadassa Medical School, Jerusalem 91120, Israel
| | - Stanislav Kler
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel, The Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel and Department of Hematology, Hebrew University–Hadassa Medical School, Jerusalem 91120, Israel
| | - Roi Asor
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel, The Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel and Department of Hematology, Hebrew University–Hadassa Medical School, Jerusalem 91120, Israel
| | - Ariella Oppenheim
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel, The Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel and Department of Hematology, Hebrew University–Hadassa Medical School, Jerusalem 91120, Israel
| | - Uri Raviv
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel, The Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel and Department of Hematology, Hebrew University–Hadassa Medical School, Jerusalem 91120, Israel
| | - Daniel Harries
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel, The Fritz Haber Research Center, The Hebrew University, Jerusalem 91904, Israel and Department of Hematology, Hebrew University–Hadassa Medical School, Jerusalem 91120, Israel
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44
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Strong and Weak Polyelectrolyte Adsorption onto Oppositely Charged Curved Surfaces. POLYELECTROLYTE COMPLEXES IN THE DISPERSED AND SOLID STATE I 2013. [DOI: 10.1007/12_2012_183] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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45
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Mahalik JP, Muthukumar M. Langevin dynamics simulation of polymer-assisted virus-like assembly. J Chem Phys 2012; 136:135101. [PMID: 22482588 DOI: 10.1063/1.3698408] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Starting from a coarse grained representation of the building units of the minute virus of mice and a flexible polyelectrolyte molecule, we have explored the mechanism of assembly into icosahedral structures with the help of Langevin dynamics simulations and the parallel tempering technique. Regular icosahedra with appropriate symmetry form only in a narrow range of temperature and polymer length. Within this region of parameters where successful assembly would proceed, we have systematically investigated the growth kinetics. The assembly of icosahedra is found to follow the classical nucleation and growth mechanism in the absence of the polymer, with the three regimes of nucleation, linear growth, and slowing down in the later stage. The calculated average nucleation time obeys the laws expected from the classical nucleation theory. The linear growth rate is found to obey the laws of secondary nucleation as in the case of lamellar growth in polymer crystallization. The same mechanism is seen in the simulations of the assembly of icosahedra in the presence of the polymer as well. The polymer reduces the nucleation barrier significantly by enhancing the local concentration of subunits via adsorbing them on their backbone. The details of growth in the presence of the polymer are also found to be consistent with the classical nucleation theory, despite the smallness of the assembled structures.
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Affiliation(s)
- J P Mahalik
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
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46
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Lošdorfer Božič A, Siber A, Podgornik R. How simple can a model of an empty viral capsid be? Charge distributions in viral capsids. J Biol Phys 2012; 38:657-71. [PMID: 24615225 PMCID: PMC3473132 DOI: 10.1007/s10867-012-9278-4] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2012] [Accepted: 07/13/2012] [Indexed: 12/21/2022] Open
Abstract
We investigate and quantify salient features of the charge distributions on viral capsids. Our analysis combines the experimentally determined capsid geometry with simple models for ionization of amino acids, thus yielding a detailed description of spatial distribution for positive and negative charges across the capsid wall. The obtained data is processed in order to extract the mean radii of distributions, surface charge densities, as well as dipole moment densities. The results are evaluated and examined in light of previously proposed models of capsid charge distributions, which are shown to have to some extent limited value when applied to real viruses.
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Affiliation(s)
- Anže Lošdorfer Božič
- Department of Theoretical Physics, Jožef Stefan Institute, 1000, Ljubljana, Slovenia,
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47
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Jin Z, Wu J. Density functional theory for encapsidated polyelectrolytes: a comparison with Monte Carlo simulation. J Chem Phys 2012; 137:044905. [PMID: 22852653 DOI: 10.1063/1.4737931] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
Genome packaging inside viral capsids is strongly influenced by the molecular size and the backbone structure of RNA∕DNA chains and their electrostatic affinity with the capsid proteins. Coarse-grained models are able to capture the generic features of non-specific interactions and provide a useful testing ground for theoretical developments. In this work, we use the classical density functional theory (DFT) within the framework of an extended primitive model for electrolyte solutions to investigate the self-organization of flexible and semi-flexible linear polyelectrolytes in spherical capsids that are permeable to small ions but not polymer segments. We compare the DFT predictions with Monte Carlo (MC) simulation for the density distributions of polymer segments and small ions at different backbone flexibilities and several solution conditions. In general, the agreement between DFT and MC is near quantitative except when the simulation results are noticeably influenced by the boundary effects. The numerical efficiency of the DFT calculations makes it promising as a useful tool for quantification of the structural and thermodynamic properties of viral nucleocapsids in vivo and at conditions pertinent to experiments.
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Affiliation(s)
- Zhehui Jin
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, USA
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48
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Bally M, Dimitrievski K, Larson G, Zhdanov VP, Höök F. Interaction of virions with membrane glycolipids. Phys Biol 2012; 9:026011. [PMID: 22475581 DOI: 10.1088/1478-3975/9/2/026011] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
Cellular membranes contain various lipids including glycolipids (GLs). The hydrophilic head groups of GLs extend from the membrane into the aqueous environment outside the cell where they act as recognition sites for specific interactions. The first steps of interaction of virions with cells often include contacts with GLs. To clarify the details of such contacts, we have used the total internal reflection fluorescence microscopy to explore the interaction of individual unlabelled virus-like particles (or, more specifically, norovirus protein capsids), which are firmly bound to a lipid bilayer, and fluorescent vesicles containing glycosphingolipids (these lipids form a subclass of GLs). The corresponding binding kinetics were earlier found to be kinetically limited, while the detachment kinetics were logarithmic over a wide range of time. Here, the detachment rate is observed to dramatically decrease with increasing concentration of glycosphingolipids from 1% to 8%. This effect has been analytically explained by using a generic model describing the statistics of bonds in the contact area between a virion and a lipid membrane. Among other factors, the model takes the formation of GL domains into account. Our analysis indicates that in the system under consideration, such domains, if present, have a characteristic size smaller than the contact area between the vesicle and the virus-like particle.
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Affiliation(s)
- M Bally
- Department of Applied Physics, Chalmers University of Technology, S-412 96 Göteborg, Sweden
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49
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Ni P, Wang Z, Ma X, Das NC, Sokol P, Chiu W, Dragnea B, Hagan M, Kao CC. An examination of the electrostatic interactions between the N-terminal tail of the Brome Mosaic Virus coat protein and encapsidated RNAs. J Mol Biol 2012; 419:284-300. [PMID: 22472420 DOI: 10.1016/j.jmb.2012.03.023] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2011] [Revised: 03/17/2012] [Accepted: 03/26/2012] [Indexed: 10/28/2022]
Abstract
The coat protein of positive-stranded RNA viruses often contains a positively charged tail that extends toward the center of the capsid and interacts with the viral genome. Electrostatic interaction between the tail and the RNA has been postulated as a major force in virus assembly and stabilization. The goal of this work is to examine the correlation between electrostatic interaction and amount of RNA packaged in the tripartite Brome Mosaic Virus (BMV). Nanoindentation experiment using atomic force microscopy showed that the stiffness of BMV virions with different RNAs varied by a range that is 10-fold higher than that would be predicted by electrostatics. BMV mutants with decreased positive charges encapsidated lower amounts of RNA while mutants with increased positive charges packaged additional RNAs up to ∼900 nt. However, the extra RNAs included truncated BMV RNAs, an additional copy of RNA4, potential cellular RNAs, or a combination of the three, indicating that change in the charge of the capsid could result in several different outcomes in RNA encapsidation. In addition, mutant with specific arginines changed to lysines in the capsid also exhibited defects in the specific encapsidation of BMV RNA4. The experimental results indicate that electrostatics is a major component in RNA encapsidation but was unable to account for all of the observed effects on RNA encapsidation. Thermodynamic modeling incorporating the electrostatics was able to predict the approximate length of the RNA to be encapsidated for the majority of mutant virions, but not for a mutant with extreme clustered positive charges. Cryo-electron microscopy of virions that encapsidated an additional copy of RNA4 revealed that, despite the increase in RNA encapsidated, the capsid structure was minimally changed. These results experimentally demonstrated the impact of electrostatics and additional restraints in the encapsidation of BMV RNAs, which could be applicable to other viruses.
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Affiliation(s)
- Peng Ni
- Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, IN 47405, USA
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Polymers under Confinement. ADVANCES IN CHEMICAL PHYSICS 2012. [DOI: 10.1002/9781118180396.ch4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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