A structural model for the Coronavirus
Federico Coscio,∗,†Alejandro D. Nadra,‡and Diego U. Ferreiro∗,¶
†Facultad de Arquitectura y Urbanismo, Universidad Cat´olica de Salta, Salta, Argentina.
‡Instituto de Biociencias, Biotecnologa y Biologa Traslacional IB3, Facultad de Ciencias
Exactas y Naturales, Universidad de Buenos Aires-CONICET, Buenos Aires, Argentina..
¶Protein Physiology Lab, Dep de Qu´ımica Biol´ogica, Facultad de Ciencias Exactas y
Naturales, Universidad de Buenos Aires-CONICET-IQUIBICEN, Buenos Aires, Argentina.
E-mail: firstname.lastname@example.org; email@example.com
Phone: (++54 +9387) 5351856; (++54 +11) 4576-3300
arXiv:2005.12165v1 [q-bio.BM] 25 May 2020
We propose a mesoscale model structure for the coronavirus nucleocapsid, assem-
bled from the high resolution structures of the basic building blocks of the N-protein,
CryoEM imaging and mathematical constraints for an overall quasi-spherical particle.
The structure is a truncated octahedron that accommodates two layers: an outer shell
composed of triangular and quadrangular lattices of the N-terminal domain and an in-
ner shell of equivalent lattices of coiled parallel helices of the C-terminal domain. The
model is consistent with the dimensions expected for packaging large viral genomes and
provides a rationale to interpret the apparent pleomorphic nature of coronaviruses.
Keywords: covid ; structure ; capsid ; tessellation ; morphology
“I want to ﬁnd happiness in the tiniest of things and I want to try to do what I’ve been wanting to
do for so long, that is, to copy these inﬁnitesimally small things as precisely as possible and to be
aware of their size.” M.C. Escher
The coronavirus (CoV) N protein is a multifunctional element that binds the viral RNA and
forms the major component of the ribonucleoprotein (RNP) forming the virion core. An important
piece of missing information about CoVs lies in the diﬃculty in solving the atomic structure of the
RNP complex, which has been hindered by its low solubility and the labile nature of the full-length
N protein1. N protein is composed of three distinct and highly conserved domains: two structural
and independently folded regions, N terminal domain (NTD, ∼180 amino acids) and C-terminal
domain (CTD, ∼160 amino acids), that are separated by an intrinsically disordered region (LKR,
∼70 amino acids). Self-association of the N protein has been observed in many viruses, and is
required for the formation of the viral capsid2. High resolution structures of both NTD and CTD
in various crystal forms are available3.
The current virion model of CoVs depicts a roughly spherical pleomorphic particle that shows
variations in size (80120 nm) and shape (reviewed in4). The RNP is surrounded by a lipidic
envelope of unusual thickness (7.8 nm), almost twice that of a typical biological membrane 5.
Early studies showed that samples in which the viral envelope was disrupted and the inner content
released, RNPs from several CoVs appear to have helical symmetry6. However, under certain
conditions, intermediate spherical nucleocapsids have been reported7,8 . These structures, which
showed polygonal proﬁles, were devoid of S protein and lipids and, in addition to RNA and the N
protein, contained the M protein. These assemblies were suggested to represent an additional viral
structure: a shelled core, possibly even icosahedral8, that would enclose the helical RNP.
As was early noted by Crick and Watson, viruses should exhibit a high degree of symmetry as
a consequence of genetic economy, the limited capacity in the viral genome to code for the proteins
forming the capsid9. Caspar and Klug extended this idea by introducing the principle of quasi-
equivalence10 , that allows larger viruses to form, requiring even smaller relative portions of their
genomic sequences to code for their capsids. Recently, Twaroc and Luque showed that this theory is
a special case of an overarching design principle for icosahedral, as well as octahedral, architectures
that can be formulated in terms of the Archimedean lattices and their duals11 . The basic symmetry
rules imply a general principle whenever a structure of a deﬁnitive size and shape has to be built
up from smaller subunits12 , the packing arrangements have to be repeated and hence the subunits
are likely to be related by symmetry operations9. Spherical viruses must be contained in one of
the three possible cubic point groups: tetrahedron, cube/octahedron, dodecahedron/icosahedron.
Here we built a mesoscale model for the CoVs nucleocapsid by bridging a bottom up approach
from the high resolutions structures of NTD and CTD and a top-down approach from mathematical
models of quasi-spherical particles.
Polyhedral approximations to the components
Modularity is a necessary condition to construct form starting from basic building blocks13 . Struc-
tural proteins must hence combine in modules that obey certain types of geometries and exist as
monomers, dimers, trimers, etc14 . There are limited possibilities to build structures that are
close to spherical and that optimize resilience. These can be algebraically constructed and can be
expressed as three-dimensional shapes with sets of regular polyhedra, its truncations, duals and
geodesics. These polyhedra have three algebraic origins: the icosahedral, octahedral and tetra-
hedral, and its capacities to tessellate the bi and tri-dimensional space. As far as our current
understanding goes, most of the viruses adopt an eﬃcient strategy, that of the icosahedron, that
can get close to sphericity with its 20 facets15 . Examples of even more eﬃcient forms include
the icosidodecahedron (32 facets), and its dual, the rhombic triacontahedron (30 facets). The oc-
tahedral and the hexahedral geometries are algebraically bonded and are capable of generating
a set of polyhedra by truncation and geodesic iteration that occupy the volume very close to a
sphere. Given their algebraic origin, these are tillable by self- similar building blocks and can be
modulated16 . An overview of the model we propose is presented in Figure 1.
Figure 1: Overall conﬁguration of the nucleocapsid model. Two concentric shells of a trun-
cated octahedron are built by the globular domains of the N protein: NTD tessellates the
external facets and CTD packs the internal shell by winding a continuous coil. The disor-
dered region LKR connects the two polyhedra.
There is a fundamental characteristic that gives the octahedral geometry a preference for CoVs
RNP structure. This geometry allows the polyhedra to be constructed with a continuous linear coil
winding, that is to say one linear element composed of identical modules that, in the case of RNP,
is a large tubular helicoid that preserves the long, continuous, RNA chain. The truncated vertex
of the octahedron is bidimensionally tillable in a linear and periodic manner. On the contrary, the
pentagonal truncated vertex of the icosahedron is only tillable by non linear, aperiodic structures
and thus cannot be built with a linear, modulated, coil winding. Accordingly, CTD can conform
helices that have akin geometry to the octahedron, constructing threads that can turn at 135◦
preserving the helical constitution.
The NTD (pdb 6M3M) has an asymmetric unit of ∼4.2nm along its longest axis, and can form a
tetramer with an approximated triangular shape (Fig. 2b). Notably, NTD can also form a tetramer
with a ﬂat square shape (pdb 6VYO, Fig. 2c).
According to CryoEM experiments, the average diameter of the internal part of the mature CoVs
virion is ∼100nm. Electron density was observed at a distance of ∼15nm from the membrane, with
a depth of ∼25nm17 . For the external shell, the edge of the non-truncated octahedron is 70nm, a
diagonal distance of 76nm, and a diameter of 98.9nm for the sphere that inscribes the octahedron.
The ordering of the hexagonal facets of the truncated octahedron are modulated by triangles whose
geometric centers are 5nm apart (green dots in Fig. 2). Each tetramer coincides with two triangles
of the equilateral tessellation, that forms without superimposition in a complex form that leaves
two monomers pointing outwards and two monomers inwards (Fig. 2b). The hexagonal facet is
formed with 6x4 modules and the square facet by 4x4 modules (Fig. 1 and Fig. 2a), making a grand
total of 2752 monomers of NTD. Triangular paracrystalline lattices were observed by CryoEM that
are compatible with these dimensions17 .
When disrupted, the virions release debris with tubular geometries of 9 to 15nm wide and hundreds
of nm length5,6 . Intact specimen observations show that the major part of the RNP locates ∼25nm
on the internal side17 . Proteins near the viral membrane are arranged in overlapping lattices
surrounding a disordered core.18 Atomic densities at these depths revealed periodic patterns that
Figure 2: Illustration of the external shell. A) NTD can tesselate both the hexagonal and the
square facets of the truncated octahedron. B) high resolution structures of the NTD tetramer
(pdb 6M3M) assembled in a triangular lattice (green dots). Two tetramers conﬁgure the
rhomb marked in red. C) high resolution structure of NTD tetramer (pdb 6VYO) in the
quadrangular conﬁguration that tessellates the square facets.
can be interpreted as romboidal, triangular and quadrangular shapes, but no evidence of icosahedral
geometry was found17,18 .
CTD domain is an obligated dimer, rotationally symmetric C1.2.1, with a major length of
5.6nm (pdb 2CJR). It can be conﬁgured in the form of an octamer of two anti parallel plates in
a butterﬂy form of 10 nm wide, with an angle of ∼45◦between dimers (Fig. 3a). This structure
can also accommodate 2 types of rotations of 90◦and 45◦between modules (Fig. 3c). CTD can
thus conform threads that have akin geometry to the octahedron, constructing helices that turn
the direction in 135◦preserving the helical constitution (Fig. 3c). The trihedral angle between the
hexagonal and square facets of the truncated octahedron is precisely 135◦. An identical turn along
the helix locates the tube 90◦to the original direction (Fig. 3c).
The proposed structure for the packaging of RNP inside the virion consists of tubular arrange-
ments of ∼10nm wide helices formed by CTD (Fig. 3d). These linear orderings are modulated in
segments of ∼8nm for each CTD octamer and 4nm for the tetramers (Fig. 3a). The hexagonal
facet is composed of 6x4 and the square facet by 4x4 modules (Fig. 1). There are 8 hexagons
composed of 74 CTD tetramers and 6 squares composed of 16 CTD tetramers. The winding of the
helicoid is completed with 2752 CTD, with a linear extension of RNP of ∼11000nm, coincident with
the expected size for packing the complete CoV genome. The helicoidal assemblies that form the
winding of the helices conform with the structure of the NTD outer shell in the form of a truncated
octahedron, such that they contain n-1 triangular modules in each level of the hexagonal facets as
they approach the vertices (Fig. 4). The packing is such that the tubular arrangements of 10nm
stack 2.5nm, leaving 5nm for each level.
Relations in between shells
Since the CTD modules are 4nm and the NTD modules are 5nm apart, the polyhedron constructed
by NTD is 20% larger. The thickness of the facets in the NTD shell is 4nm. Taking into account
that the space in between the external facets of both polyhedra is 7nm, the interstitial space is
about 3nm. NTD have 2nm protuberances to the inside that pack precisely against the tubular
levels of CTD (Fig. 4). Since both NTD and CTD are connected by the LKR region, and both
Figure 3: Conﬁguration of the internal shell. A) CTD octamers form a butterﬂy shaped
module (pdb 2CJR) that is represented in diﬀerent colors (B) according to their orientation.
C) packing of CTD modules allow for the construction of helices that can turn 135◦preserving
the helical constitution. D) consecutive 135◦turns locates the helix 90◦to the original
globular domains have been shown to interact with RNA 1, we speculate that the interstitial space
is ﬁlled with the LKR and RNA that is winded along the CTD helix.
Figure 4: Artistic rendering of the nucleocapsid structure. A) the membrane and the S and
M proteins are depicted in blue colors. The external shell is represented with a transparent
brown truncated octahedron. The interior shows the continuos coil packing of the blue and
cyan CTD helices. B) High resolution structures of the NTD modules (2 tetramers) and
CTD modules (4 dimers) linked by LKR regions.
Cryo electron tomography showed that the coronavirus nucleocapsid is separated from the
envelope by a gap, which has revealed to contain thread-like densities that connect the protein
density on the inner face of the viral membrane to a two-dimensionally ordered ribonucleoprotein
layer5. Focal pairs revealed the existence of an extra internal layer that was attributed to the
M protein, but that is compatible with the composite model we propose. Moreover, nucleoprotein
densities were observed as a paracrystalline RNP shell, and may be partially organized at points
of contact of the RNP lattice. The distribution of density in the viral core was consistent with a
membrane-proximal RNP lattice formed by local approaches of the coiled ribonucleoprotein5,17 . In
the interior of the particles, coiled structures and tubular shapes were observed, consistent with a
helical CTD model. The ribonucleoprotein appears to be extensively folded onto itself, assuming a
compact structure that tends to closely follow the envelope at a distance of 4 nm5. This indicates
the existence of an additional layer that would confer the virion envelope its remarkable thickness.
Viral nucleocapsids must obey a structural strategy that eﬃciently packs a long continuous chain
of nucleic acid in an ordered manner, and thus it needs to adopt a consistent morphology. At
the same time it is biologically required to have the versatility to disassemble and reassemble
the components, in this case a tubular helicoidal packing of RNA and protein. We propose that
these cannot be arbitrarily packed inside the virion but must be modulated, implying structural
forms that are robustly built. The model we present is compatible with the known high resolution
structures of the basic elements of N protein, their stoichiometry, and the lattice densities observed
by cryoEM and cryo electron tomography. The octahedral geometry was previously observed in
the bacteriophage MS2 (pdb 2VTU19 ), a smaller nucleocapsid with no membrane. However, many
EM studies did not observe a clear octahedral nucleocapsid as we propose, but rather describe
roughly spherical pleomorphic particles. We propose that these observations can be reinterpreted
under the current model. The apparent pleomorphism of CoVs may not be caused by RNP, but
the transformations of the membrane that surrounds the nucleocapsid. If the capsid is octahedral,
the membrane may ﬂatten in the facets, giving the impression of strong deformations (Fig. 5).
Recall that in CoVs the distance between the membrane and the nucleocapsid may reach 15nm of
untidy regions, and thus this distance could vary between the vertices of the truncated octahedron
and be much closer than the centers of the facets. These can be the places where N interacts
with the M protein, a known necessary component for virion assembly. Coronavirus N proteins are
appealing drug targets against coronavirus-induced diseases. A variety of compounds targeting the
coronavirus nucleocapsid protein have been developed and many of these show potential antiviral
Figure 5: Apparent pleomorphism of coronavirus. Diﬀerent perspectives of the model are
shown superimposed to the electron microscopy densities observed by Almeida et .al21 in
panels A) and E) and by Neuman et. al.17 in the other panels. Scale bar is 100nm.
This work was supported by the Consejo Nacional de Investigaciones Cient´ıﬁcas y T´ecnicas de
Argentina (CONICET), the Agencia Nacional de Promoci´on Cient´ıﬁca y Tecnol´ogica (ANPCyT),
the Universidad de Buenos Aires and NASA Astrobiology Institute. ADN and DUF are Career
Investigators of CONICET.
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