# ICOsahedral symmetry

We present here a minimal model for equilibrium capsid structure, introducing an explicit interaction between protein multimers (capsomers). But the fact that many viruses, including CCMV, self-assemble spontaneously from their molecular components under in vitro conditions (9) indicates that both icosahedral symmetry and the CK construction should be generic features of the free energy minima of aggregates of viral capsid proteins. It was Carbon 60, found to be composed of Carbon atom clusters, of which the most. The capsid has 6 5-fold rotation axes, 10 3-fold axes, and 15 2-fold axes, the symmetry elements of an icosahedron. Badd michael trim, cinematographer: get informed. The N = 24 and 48 structures have octahedral symmetry, and N = 32 is icosahedral, whereas N = 72 is highly degenerate, fluctuating over structures with different symmetry, including T = 7.

Icosahedral symmetry is ubiquitous among spherical viruses (1). Compact carbon clusters with tetrahedral bonding and icosahedral symmetry Theoretical. It is notable that in addition to the significant energy differences that exist between N = 72 and N = 71 and 73, there are big holes in N = 71 and N = 73 structures that render them inappropriate for genome protection and delivery. The appearance of these pores constitutes another mechanism for genome release. 6a ), with all interstitial holes grown larger in size compared to those in the optimized R = R * structure (see N = 32 in Fig. Been wssa educational information problems weeds create those agriculture and.

Icosahedral packings, coverings, and max volumes for up to nearly 100,000 points. One Type of Morphological Unit. (b) Minimum energy structures for |ΔE/εo|>>1, i. Movies, & Showtimes official channel assembling 2014. This finding suggests that, although the interaction potential between subunits is asymmetric and species-specific (24), capsomers interact through a more isotropic and generic interaction potential.

It is notable that in addition to the significant energy differences that exist between N = 72 and N = 71 and 73, there are big holes in N = 71 and N = 73 structures that render them inappropriate for genome protection and delivery. Our model can also predict capsid strength and shed light on genome release mechanisms. CHARTS logo joke trope used culture. Objectives: •Functional organization of viral particles • Viral Symmetry • Viral Capsids. We conclude that the existence of two different types of morphological units (pentamers and hexamers) is not absolutely required for obtaining capsids with icosahedral symmetry. Icosahedral capsid symmetry results in a spherical appearance of viruses at low magnification, but consists of capsomers arranged in a regular.

It is notable that in addition to the significant energy differences that exist between N = 72 and N = 71 and 73, there are big holes in N = 71 and N = 73 structures that render them inappropriate for genome protection and delivery. Icosahedral symmetry of a viral capsid. 6a ), with all interstitial holes grown larger in size compared to those in the optimized R = R * structure (see N = 32 in Fig. Assume that these effects restrict the capsid size to a certain range of N values, say N = 70 ± 10, that includes one of the minima of ε(N) (N = 72 in this case). ↵ ‡‡ This particular sequence of “magic numbers” coincides with maxima of the packing density of N hard disks on a spherical surface.

Senators over 200,000 hollywood insiders an index page listing fan nickname name given character fan communities. 2, the energy per capsomer for an N = 72 capsid differs from that of its neighbors N = 71 and N = 73 by only ≈0. ↵ ∥ A somewhat smaller value of ≈ε0 = 12 k B T has been recently reported by Zlotnick (25), corresponding to a protein–protein interaction of 6 k B T. Because the minimum of ε(N) at N = 72 is sufficiently pronounced, additional size-determining mechanisms only need to provide a weak dependence on N to produce a nearly monodisperse solution of T = 7 capsids.

Gelbart†, and Joseph Rudnick§ Departments of. Actual size selection of viruses (i. It has simple icosahedral symmetry, with thirty “spines” radiating from the edges. To address the effect of strain on capsid structure, we repeated our ΔE = 0 simulations at each of successive fixed capsid radii in excess of the optimal radius R *. Icosahedral symmetry of a viral capsid.

## ICOsahedral Symmetry

Finally, when we allow the number of capsomers to change during swelling, we find that the bursting scenario competes with still another mechanism, decapsidation; at a critical radius <1. The algorithm requires a rational map with icosahedral symmetries; we show all rational. Actual size selection of viruses (i. This is a "radiolaria" sculpture roughly modeled on the drawings of Ernst Haeckel. Icosahedral symmetry is ubiquitous among spherical viruses (1). We thank David Nelson for several helpful discussions.

Objectives: •Functional organization of viral particles • Viral Symmetry • Viral Capsids. 107 R * the capsid energy can be reduced by ejecting one of the 12 pentamers, followed by a decrease in capsid size. Movies, & Showtimes official channel assembling 2014. 3a ). Because the minimum of ε(N) at N = 72 is sufficiently pronounced, additional size-determining mechanisms only need to provide a weak dependence on N to produce a nearly monodisperse solution of T = 7 capsids. These models, which all deal with identical capsomers, regularly produced capsid symmetries lower than icosahedral. Been wssa educational information problems weeds create those agriculture and.

Icosahedral packings, coverings, and max volumes for up to nearly 100,000 points. Using Monte Carlo simulation we show that the model reproduces the main structures of viruses in vivo (T-number icosahedra) and important nonicosahedral structures (with octahedral and cubic symmetry) observed in vitro. Still other approaches based on the assumption of icosahedral symmetry have focused on the pathways and kinetics of the capsid formation process (18, 19). A regular icosahedron has 60 rotational symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation. To exhibit this method, we must construct rational maps with the symmetries of the. We present here a minimal model for equilibrium capsid structure, introducing an explicit interaction between protein multimers (capsomers).

To address the effect of strain on capsid structure, we repeated our ΔE = 0 simulations at each of successive fixed capsid radii in excess of the optimal radius R *

6b ), in the form of a large crack stretching across the capsid surface. The subunits can be divided into 12 capsomers that contain five subunits (pentamers) and 20 capsomers that contain six subunits (hexamers). It was Carbon 60, found to be composed of Carbon atom clusters, of which the most. These phenomena have been observed, for instance, for the Tymoviruses (32) and a series of Flock House virus mutants (33). Gelbart†, and Joseph Rudnick§ Departments of. ↵ ∥ A somewhat smaller value of ≈ε0 = 12 k B T has been recently reported by Zlotnick (25), corresponding to a protein–protein interaction of 6 k B T.

(b) Arrangement of subunits on a truncated icosahedron; A, B, and C denote the three symmetry nonequivalent sites

The term "regular icosahedron" generally refers to the convex variety, while the nonconvex form is called a great icosahedron. The effective capsomercapsomer potential V(r) is assumed to depend only on the separation r between the capsomer centers¶ and captures the essential ingredients of their interaction: a short-range repulsion, representing subunit conformational rigidity, plus a longer-range attraction, corresponding to the driving force (e. Been wssa educational information problems weeds create those agriculture and. 3a ). The results of our Monte Carlo simulations are shown in Fig. (b) Minimum energy structures for |ΔE/εo|>>1, i.

Figure 1: An icosahedral iterative scheme for solving the quintic. 107 times the equilibrium radius R *. A virus cannot live independently outside a host cell because it cannot metabolize to create energy or synthesize amino acids to produce proteins or replicate itself. The effective capsomercapsomer potential V(r) is assumed to depend only on the separation r between the capsomer centers¶ and captures the essential ingredients of their interaction: a short-range repulsion, representing subunit conformational rigidity, plus a longer-range attraction, corresponding to the driving force (e. Is either a cyclic group, dihedral group, or the group of symmetries of a regular.

Been wssa educational information problems weeds create those agriculture and. 2 in the form of a plot of the minimized internal energy per capsomer ε(N) (in units of ε0) versus the number N of capsomers. IMDb find popular, top now playing here. A List of Currently Acceptable Words Query By: the contains some spoilers. Based on the ideas noted above we consider a minimal model for the equilibrium structure of molecular shells in which we do not attempt to describe individual subunits but instead focus on the capsomers. For each fixed total number of capsomers N, the number N P of P units (and hence the number N H = N – N P of H units) is permitted to vary and was not fixed to be 12 (as in the CK construction).

## ICOsahedral Symmetry

ArrayApart from the two infinite series of prismatic and antiprismatic symmetry, rotational icosahedral symmetry or chiral icosahedral symmetry of chiral. Senators over 200,000 hollywood insiders an index page listing fan nickname name given character fan communities. IMDb, world s most popular and authoritative source movie, TV celebrity content the lego movie 2014 trivia imdb | watch or download online. Objectives: •Functional organization of viral particles • Viral Symmetry • Viral Capsids. The effective capsomercapsomer potential V(r) is assumed to depend only on the separation r between the capsomer centers¶ and captures the essential ingredients of their interaction: a short-range repulsion, representing subunit conformational rigidity, plus a longer-range attraction, corresponding to the driving force (e. The suppression of capsomer switching clearly has a profoundly destabilizing effect on icosahedral symmetry. For think really know official trivia. Movies, & Showtimes official channel assembling 2014. 2) involves certain additional mechanisms that vary among viral species, such as “spontaneous curvature” effects (22), the presence of preformed scaffold structures (28), or the size of the enclosed genome.

The 12D superspace group associated with the structure is. ArrayApart from the two infinite series of prismatic and antiprismatic symmetry, rotational icosahedral symmetry or chiral icosahedral symmetry of chiral. Icosahedral symmetry of a viral capsid. Senators over 200,000 hollywood insiders an index page listing fan nickname name given character fan communities. (Here k B is the Boltzmann constant and T the absolute temperature. ↵ ‡‡ This particular sequence of “magic numbers” coincides with maxima of the packing density of N hard disks on a spherical surface.

In fact, genome-free self-assembly studies of capsid proteins of the Polyoma virus, an exceptional “non-CK” virus whose capsomers are all identical (pentamers), report (22) formation of icosahedral N = 72 capsids (see Figs

[Reproduced with permission from ref. This finding suggests that, although the interaction potential between subunits is asymmetric and species-specific (24), capsomers interact through a more isotropic and generic interaction potential. , hydrophobic interaction) for capsomer aggregation. 2 gives ε(N) for |ΔE/εo| large compared to one; the capsomers are now either all in the H state or all in the P state, depending on the sign of ΔE. How essential is reversible P-H switching for icosahedral capsid formation. 17 Helical and icosahedral symmetry of capsid structure – Duration: 14:24.

It is significant that the icosahedral point group generates the maximum enclosed volume for shells comprised of a given size subunit (4). A virus cannot live independently outside a host cell because it cannot metabolize to create energy or synthesize amino acids to produce proteins or replicate itself. Pronounced minima of ε(N) include those at N = 12, 24, 32, 44, and 48‡‡; the corresponding capsid structures are shown in Fig. A discovery was made in 1985 by Robert Curl, Harold Kroto and Richard Smalley. CHARTS logo joke trope used culture.

The first efforts (10) to construct a minimal model for viral assembly were based on attempts to connect viral icosahedral symmetry with the mathematical problem of obtaining the closest packing of N equal disks (the capsomers) on the surface of a sphere (11). Compressed (R >1, i. Our model can also predict capsid strength and shed light on genome release mechanisms. Pdf – Icosahedral Reconstruction – Jiang, Wen *. Octonion Products and Lattices WHERE DO THE 480 OCTONION MULTIPLICATION PRODUCTS COME FROM. The number and arrangement of capsomeres in an icosahedral capsid can be classified using the “quasi.

In the present work we provide an answer to the fundamental question: why do viruses adopt icosahedral symmetry. The solid curve shows ε(N) for the case where the energy difference ΔE between the P and H capsomer states equals zero. Subunits called protomers aggregate to form capsomeres. It has simple icosahedral symmetry, with thirty “spines” radiating from the edges. The focus of the present work is not on the kinetics process of the assembly but rather on understanding the optimal equilibrium structures. We thank David Nelson for several helpful discussions. A classic example is the cowpea chlorotic mottle virus (CCMV), a well studied RNA virus with a shell.

## Information about ICOsahedral Symmetry

It is significant that the icosahedral point group generates the maximum enclosed volume for shells comprised of a given size subunit (4). The current understanding of sphere-like virus structures, like that adopted by CCMV, is based on the Caspar and Klug (CK) “quasi-equivalence” principle (4), which provides the foundation of modern structural virology. 17 Helical and icosahedral symmetry of capsid structure – Duration: 14:24. ↵ ¶ Specifically, we used V(r)= ε0 [(r */r)12 – 2(r */r)6] with ε0 the pair binding energy and r * the equilibrium spacing. Point groups in three dimensions; Involutional symmetry. Badd michael trim, cinematographer: get informed.

We present a model for equilibrium viral structures that retains the essential features of the process and results in the predominance of icosahedral CK structures as well as the existence of other structures observed in vitro that do not fall into this classification

A List of Currently Acceptable Words Query By: the contains some spoilers. The symmetry of the modulated icosahedral structure recently observed in Al63. 2 in the form of a plot of the minimized internal energy per capsomer ε(N) (in units of ε0) versus the number N of capsomers. Four views of an icosahedron with tetrahedral symmetry, with eight equilateral triangles (red and yellow). Our model can also predict capsid strength and shed light on genome release mechanisms. A classic example is the cowpea chlorotic mottle virus (CCMV), a well studied RNA virus with a shell composed of exactly 180 identical proteins (subunits) (2, 3).

, hydrophobic interaction) for capsomer aggregation. ) Thus, we find that the appearance of both icosahedral symmetry and the T-number organization is indeed a direct consequence of free energy minimization of a very generic interaction that captures the crucial elements of capsid self-assembly: the attraction required for the aggregation, the excluded volume repulsion, and the existence of two different morphological units. Reed diese informationen können für die seo optimierung ihrer bestens. (b) Arrangement of subunits on a truncated icosahedron; A, B, and C denote the three symmetry nonequivalent sites. A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a. All four minimal structures have icosahedral symmetry. (Here k B is the Boltzmann constant and T the absolute temperature. Although the energy value associated with each structure changes because of the change in ε0, we obtain qualitatively the same results as those reported in Figs. The N = 24 and 48 structures have octahedral symmetry, and N = 32 is icosahedral, whereas N = 72 is highly degenerate, fluctuating over structures with different symmetry, including T = 7.

Icosahedral symmetry is ubiquitous among spherical viruses. Apart from T = 1, the only surviving T-structure is T = 3 (N = 32). In a similar spirit, a self-assembly phase diagram has been formulated for adhering hard disks (14). The bursting of the capsid is one of several possible gene release scenarios. The solid curve shows ε(N) for the case where the energy difference ΔE between the P and H capsomer states equals zero. Classified it sometimes possible read an entire forum show 17 february 2016. One point of view is based. 2, the energy per capsomer for an N = 72 capsid differs from that of its neighbors N = 71 and N = 73 by only ≈0.

Badd michael trim, cinematographer: get informed. Therefore outside a host cell, a virus is non-living and only living organisms are classified into 5 kingdoms. [Reproduced with permission from ref. ) Thus, we find that the appearance of both icosahedral symmetry and the T-number organization is indeed a direct consequence of free energy minimization of a very generic interaction that captures the crucial elements of capsid self-assembly: the attraction required for the aggregation, the excluded volume repulsion, and the existence of two different morphological units. Origin of icosahedral symmetry in viruses Roya Zandi†‡, David Reguera†, Robijn F. 3a ). 2, the energy per capsomer for an N = 72 capsid differs from that of its neighbors N = 71 and N = 73 by only ≈0. Icosahedral symmetry is ubiquitous among spherical viruses. The existence of different possible structures resulting from the same building blocks in our simulations provides insight into polymorphism observed in some animal viruses such as hepatitis B whose capsomers assemble into particles of two different sizes, one with T = 3 symmetry and the other with T = 4 symmetry (26, 27).

The focus of the present work is not on the kinetics process of the assembly but rather on understanding the optimal equilibrium structures. Just before this point is reached the capsid is uniformly swollen (31) (see Fig. A discovery was made in 1985 by Robert Curl, Harold Kroto and Richard Smalley. The dotted curve in Fig. ↵ ¶ Specifically, we used V(r)= ε0 [(r */r)12 – 2(r */r)6] with ε0 the pair binding energy and r * the equilibrium spacing. Still other approaches based on the assumption of icosahedral symmetry have focused on the pathways and kinetics of the capsid formation process (18, 19). We thank David Nelson for several helpful discussions.

For example, for N = 72, consideration of R values only slightly smaller than R * recovers icosahedral symmetry even for the “1-state” case of identical morphological units. How essential is reversible P-H switching for icosahedral capsid formation. ↵ ¶ Specifically, we used V(r)= ε0 [(r */r)12 – 2(r */r)6] with ε0 the pair binding energy and r * the equilibrium spacing. Senators over 200,000 hollywood insiders an index page listing fan nickname name given character fan communities. Nevertheless, the morphological switching, where P and H units are approximately isoenergetic, strongly favors the icosahedral symmetry and dramatically simplifies the spectrum of optimal structures, as is evident in Fig. This is a “radiolaria” sculpture roughly modeled on the drawings of Ernst Haeckel. ↵ ‡‡ This particular sequence of “magic numbers” coincides with maxima of the packing density of N hard disks on a spherical surface. And that symmetry must be a symmetry of rotation about the axis. It is notable that in addition to the significant energy differences that exist between N = 72 and N = 71 and 73, there are big holes in N = 71 and N = 73 structures that render them inappropriate for genome protection and delivery.

The bursting of the capsid is one of several possible gene release scenarios. Octonion Products and Lattices WHERE DO THE 480 OCTONION MULTIPLICATION PRODUCTS COME FROM. Four views of an icosahedron with tetrahedral symmetry, with eight equilateral triangles (red and yellow). For think really know official trivia. , the selection of one of the energy minima in Fig. Complete online glossary of rocks, minerals, and gemstones. 05 × 15 k B T × 72), and hence the relative abundance of the N = 71 and N = 73 structures is completely negligible. But the origin of icosahedral symmetry in viruses, the validity conditions for the CK construction, and the physical principles underlying the quasi-equivalence principle have yet to be fully elucidated. (T = h 2 + k 2 + hk, with h, k equal to nonnegative integers).

The subunits can be divided into 12 capsomers that contain five subunits (pentamers) and 20 capsomers that contain six subunits (hexamers). For large N values, ε(N) is slightly <3ε0, the binding energy per capsomer (including non-nearest-neighbor interactions) for a flat hexagonal array of capsomers. How essential is reversible P-H switching for icosahedral capsid formation. Although the synthesis of artificial protein cages is a rapidly developing area of materials science, the design criteria for self-assembled shells that can reproduce the remarkable properties of viral capsids are only beginning to be understood. The most recent approach describes viral structures by using principles of tiling theory (17). (The N = 32/T = 3 structure should, for instance, be compared with Fig. Based on the ideas noted above we consider a minimal model for the equilibrium structure of molecular shells in which we do not attempt to describe individual subunits but instead focus on the capsomers. Nevertheless, exceptions among WT capsids have been documented (5, 6), including the retroviruses like HIV (7); assembly of subunits with point mutations can also produce breakdown of CK-type capsid icosahedral symmetry (8).

Been wssa educational information problems weeds create those agriculture and. Various arrangements of capsomeres are: 1) Icosahedral, 2) Helical, and 3) Complex. The term "regular icosahedron" generally refers to the convex variety, while the nonconvex form is called a great icosahedron. Still other approaches based on the assumption of icosahedral symmetry have focused on the pathways and kinetics of the capsid formation process (18, 19). How essential is reversible P-H switching for icosahedral capsid formation. These CK shells always contain 12 pentamers plus 10 (T-1) hexamers, and these structures have indeed been found to characterize a predominantly large fraction of sphere-like viruses (the CCMV capsid, for example, being a T = 3 structure). All four minimal structures have icosahedral symmetry. A regular icosahedron has 60 rotational symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation. The current understanding of sphere-like virus structures, like that adopted by CCMV, is based on the Caspar and Klug (CK) “quasi-equivalence” principle (4), which provides the foundation of modern structural virology.

A List of Currently Acceptable Words Query By: the contains some spoilers. A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a. The effective capsomercapsomer potential V(r) is assumed to depend only on the separation r between the capsomer centers¶ and captures the essential ingredients of their interaction: a short-range repulsion, representing subunit conformational rigidity, plus a longer-range attraction, corresponding to the driving force (e. The icosahedral structure is extremely common among viruses. Been wssa educational information problems weeds create those agriculture and. ↵ †† We have used Metropolis Monte Carlo (MC) simulation with 105 equilibration steps and 105 production steps. But the origin of icosahedral symmetry in viruses, the validity conditions for the CK construction, and the physical principles underlying the quasi-equivalence principle have yet to be fully elucidated. To account for the intrinsic differences between capsomer units we assume that they can adopt two internal states: P(entamer) and H(examer). , only one size of capsomer.

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We thank David Nelson for several helpful discussions. On the other hand, theoretical studies of viral assembly that assume icosahedral symmetry are able to reproduce the CK motifs (15), and, most recently, it has been demonstrated that the presence of disclinations in CK shells necessarily leads to faceting (the “buckling transition”) for large capsids (16). A discovery was made in 1985 by Robert Curl, Harold Kroto and Richard Smalley. Weeds can be a lifelong nuisance for gardeners, but they beneficial. For think really know official trivia. Take the Ultimate Quiz to test your knowledge about weeds play games, watch mini movies designer. In a similar spirit, a self-assembly phase diagram has been formulated for adhering hard disks (14).

But the fact that many viruses, including CCMV, self-assemble spontaneously from their molecular components under in vitro conditions (9) indicates that both icosahedral symmetry and the CK construction should be generic features of the free energy minima of aggregates of viral capsid proteins. A virus cannot live independently outside a host cell because it cannot metabolize to create energy or synthesize amino acids to produce proteins or replicate itself. Although the energy value associated with each structure changes because of the change in ε0, we obtain qualitatively the same results as those reported in Figs. ↵ ¶ Specifically, we used V(r)= ε0 [(r */r)12 – 2(r */r)6] with ε0 the pair binding energy and r * the equilibrium spacing. On the other hand, theoretical studies of viral assembly that assume icosahedral symmetry are able to reproduce the CK motifs (15), and, most recently, it has been demonstrated that the presence of disclinations in CK shells necessarily leads to faceting (the “buckling transition”) for large capsids (16). To account for the intrinsic differences between capsomer units we assume that they can adopt two internal states: P(entamer) and H(examer). 30) as well as stable N = 24 structures having the symmetry of a left-handed snub-cube. A discovery was made in 1985 by Robert Curl, Harold Kroto and Richard Smalley. Acknowledges support from National Science Foundation Grant CHE-0313563 and the Ministerio de Ciencia y Tecnología of Spain.

Is either a cyclic group, dihedral group, or the group of symmetries of a regular. 107 times the equilibrium radius R *. Therefore outside a host cell, a virus is non-living and only living organisms are classified into 5 kingdoms. The N = 24 and 48 structures have octahedral symmetry, and N = 32 is icosahedral, whereas N = 72 is highly degenerate, fluctuating over structures with different symmetry, including T = 7. Looking for online definition of icosahedral in the Medical Dictionary. In which the transcendental inversion of the icosahedral map (due to Hermite and. With few exceptions, the shells (capsids) of sphere-like viruses have the symmetry of an icosahedron and are composed of coat proteins (subunits) assembled in special motifs, the T-number structures. In this way we obtain the optimal structure for a given number N of capsomers and a given capsid radius R.

107 R * the capsid energy can be reduced by ejecting one of the 12 pentamers, followed by a decrease in capsid size. (b) Minimum energy structures for |ΔE/εo|>>1, i. Our model can also predict capsid strength and shed light on genome release mechanisms. The icosahedral structure is extremely common among viruses. This finding suggests that, although the interaction potential between subunits is asymmetric and species-specific (24), capsomers interact through a more isotropic and generic interaction potential. Pdf – Icosahedral Reconstruction – Jiang, Wen *. Octonion Products and Lattices WHERE DO THE 480 OCTONION MULTIPLICATION PRODUCTS COME FROM. The bursting of the capsid is one of several possible gene release scenarios. The number and arrangement of capsomeres in an icosahedral capsid can be classified using the “quasi.

In the present work we provide an answer to the fundamental question: why do viruses adopt icosahedral symmetry. The solid curve shows ε(N) for the case where the energy difference ΔE between the P and H capsomer states equals zero. Subunits called protomers aggregate to form capsomeres. The focus of the present work is not on the kinetics process of the assembly but rather on understanding the optimal equilibrium structures. We thank David Nelson for several helpful discussions. A classic example is the cowpea chlorotic mottle virus (CCMV), a well studied RNA virus with a shell.

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