Keplerate Ag192 Cluster with 6 Silver and 14 Chalcogenide Octahedral and Tetrahedral Shells.

Silver clusters with more than 2 concentric silver shells are scarce. Here, we enable self-assembly and crystallize SD/Ag192a, a highly symmetric silver chalcogenide cluster (SCC) with 192 silver cations in 6 shells and 136 anionic groups in 14 shells. All but 1 of these 20 concentric shells are Platonic or Archimedean solids. All have octahedral or tetrahedral symmetry and align the maximum number of their 2-, 3-, and 4-fold axes of rotational symmetry, thus identifying the cluster as a Keplerate. A rhombic dodecahedron supershell, formed from the first 3 anionic shells, is the keystone for the entire structure. But, nearly all of the edges in these polyhedral shells are too long to represent bonds. What mechanism of coordination chemistry holds the shells together? Like Na+ ions held electrostatically inside adjacent cube-shaped anionic compartments in a crystal of NaCl, individual Ag+ ions sit inside adjacent octahedron-shaped anionic compartments that fill space. Similarly, like Cl- ions in NaCl, individual anionic groups sit inside adjacent cationic (Ag+) compartments, mostly uniform polyhedra, that also fill space.

Precise Implantation of an Archimedean Ag@Cu12 Cuboctahedron into a Platonic Cu4Bis(diphenylphosphino)hexane6 Tetrahedron.

Precision loading of nanoclusters in confined spaces, which has been enthusiastically pursued in the scientific realm, is still associated with some mysteries of "how", "when", and "why". Here, we isolated two similar heterometallic cluster-in-cage compounds, [Ag@Cu12S8@Cu4(dpph)6]X (X = OH, SD/AgCu16a and X = PF6, SD/AgCu16b; SD = SunDi), by use of an antigalvanic reaction between organometallic [PhC≡CCu]n and Ph3CSH with elemental silver. Both compounds are formed by fitting an Archimedean Ag@Cu12 cuboctahedral cluster into a Platonic Cu4(dpph)6 tetrahedral cage [dpph = bis(diphenylphosphino)hexane]. The Ag@Cu12 cluster is a hollow cuboctahedral Cu12 cage filled with a central AgI atom, and all eight triangular faces of the Ag@Cu12 cuboctahedron are triply capped by eight S2- ions, four of which in a tetrahedral array further internally pillar four Cu vertices of the outer Cu4(dpph)6 tetrahedron, fixing the cluster in the cage. Both compounds can be deemed as molecular fragments excised from porous nanomaterials filled with discrete nanoclusters, thus providing more details for understanding the confined growth of atomically precise nanoclusters. Electrospray ionization mass spectrometry (ESI-MS) reveals that the AgCu16 cluster is quite stable in CH2Cl2 and can stepwise lose dpph ligand in the gas phase under increased collision energy. This work not only presents a precise aggregation of metal atoms in a confined cavity to form a cluster-in-cage compound but also provides deep insights into the binding and geometry matching between clusters and cages in one entity.

A Keplerian Ag90 nest of Platonic and Archimedean polyhedra in different symmetry groups.

Polyhedra are ubiquitous in chemistry, biology, mathematics and other disciplines. Coordination-driven self-assembly has created molecules mimicking Platonic, Archimedean and even Goldberg polyhedra, however, nesting multiple polyhedra in one cluster is challenging, not only for synthesis but also for determining the alignment of the polyhedra. Here, we synthesize a nested Ag90 nanocluster under solvothermal condition. This pseudo-Th symmetric Ag90 ball contains three concentric Ag polyhedra with apparently incompatible symmetry. Specifically, the inner (Ag6) and middle (Ag24) shells are octahedral (Oh), an octahedron (a Platonic solid with six 3.3.3.3 vertices) and a truncated octahedron (an Archimedean solid with twenty-four 4.6.6 vertices), whereas the outer (Ag60) shell is icosahedral (Ih), a rhombicosidodecahedron (an Archimedean solid with sixty 3.4.5.4 vertices). The Ag90 nanocluster solves the apparent incompatibility with the most symmetric arrangement of 2- and 3-fold rotational axes, similar to the arrangement in the model called Kepler's Kosmos, devised by the mathematician John Conway.

Three Silver Nests Capped by Thiolate/Phenylphosphonate.

Introducing phenylphosphonic acid (H2 PPA) into the Ag/tBuSH assembly system has produced a family of nanoscale-sized, high-atom number, silver thiolate/PPA nests (SD/Ag45 a, SD/Ag66 a, and SD/Ag73 a) with impressive core-shell features. SD/Ag45 a is a 45-atom ellipsoid comprised of an Ag36 shell trapping an Ag9 S2 three-bladed rotor inside. SD/Ag66 a comprises an inner rod-like Ag20 core and an outer Ag44 shell, giving a 64-atom nest. These Ag64 nests are further extended by Ag(CN)2 linkers to form a one-dimensional chain structure. SD/Ag73 a is a three-shell 73-nucleus silver nest with a central silver atom enclosed in a rhombicuboctahedron of 24 silver atoms, which is itself enclosed in the outermost shell of a rectified version of a 48-Ag octahedral Goldberg 2,0 cage. The solution behaviors and optical absorption properties of the three nests are described in detail. Of note, SD/Ag45 a and SD/Ag73 a emit in the near-infrared region and show different luminescent thermochromic behavior. This work demonstrates that the participation of H2 PPA strongly influences the structures of silver thiolate nests, thus providing a new route to fabricate and modify them in a more rational way.

Assembly of silver Trigons into a buckyball-like Ag180 nanocage.

Buckminsterfullerene (C60) represents a perfect combination of geometry and molecular structural chemistry. It has inspired many creative ideas for building fullerene-like nanopolyhedra. These include other fullerenes, virus capsids, polyhedra based on DNA, and synthetic polynuclear metal clusters and cages. Indeed, the regular organization of large numbers of metal atoms into one highly complex structure remains one of the foremost challenges in supramolecular chemistry. Here we describe the design, synthesis, and characterization of a Ag180 nanocage with 180 Ag atoms as 4-valent vertices (V), 360 edges (E), and 182 faces (F)--sixty 3-gons, ninety 4-gons, twelve 5-gons, and twenty 6-gons--in agreement with Euler's rule V - E + F = 2. If each 3-gon (or silver Trigon) were replaced with a carbon atom linked by edges along the 4-gons, the result would be like C60, topologically a truncated icosahedron, an Archimedean solid with icosahedral (Ih) point-group symmetry. If C60 can be described mathematically as a curling up of a 6.6.6 Platonic tiling, the Ag180 cage can be described as a curling up of a 3.4.6.4 Archimedean tiling. High-resolution electrospray ionization mass spectrometry reveals that {Ag3}n subunits coexist with the Ag180 species in the assembly system before the final crystallization of Ag180, suggesting that the silver Trigon is the smallest building block in assembly of the final cage. Thus, we assign the underlying growth mechanism of Ag180 to the Silver-Trigon Assembly Road (STAR), an assembly path that might be further employed to fabricate larger, elegant silver cages.

Four levels of hierarchical organization, including noncovalent chainmail, brace the mature tumor herpesvirus capsid against pressurization.

Like many double-stranded DNA viruses, tumor gammaherpesviruses Epstein-Barr virus and Kaposi's sarcoma-associated herpesvirus withstand high internal pressure. Bacteriophage HK97 uses covalent chainmail for this purpose, but how this is achieved noncovalently in the much larger gammaherpesvirus capsid is unknown. Our cryoelectron microscopy structure of a gammaherpesvirus capsid reveals a hierarchy of four levels of organization: (1) Within a hexon capsomer, each monomer of the major capsid protein (MCP), 1,378 amino acids and six domains, interacts with its neighboring MCPs at four sites. (2) Neighboring capsomers are linked in pairs by MCP dimerization domains and in groups of three by heterotrimeric triplex proteins. (3) Small (∼280 amino acids) HK97-like domains in MCP monomers alternate with triplex heterotrimers to form a belt that encircles each capsomer. (4) One hundred sixty-two belts concatenate to form noncovalent chainmail. The triplex heterotrimer orchestrates all four levels and likely drives maturation to an angular capsid that can withstand pressurization.

Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses.

The three known classes of convex polyhedron with equal edge lengths and polyhedral symmetry--tetrahedral, octahedral, and icosahedral--are the 5 Platonic polyhedra, the 13 Archimedean polyhedra--including the truncated icosahedron or soccer ball--and the 2 rhombic polyhedra reported by Johannes Kepler in 1611. (Some carbon fullerenes, inorganic cages, icosahedral viruses, geodesic structures, and protein complexes resemble these fundamental shapes.) Here we add a fourth class, "Goldberg polyhedra," which are also convex and equilateral. We begin by decorating each of the triangular facets of a tetrahedron, an octahedron, or an icosahedron with the T vertices and connecting edges of a "Goldberg triangle." We obtain the unique set of internal angles in each planar face of each polyhedron by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, and the variables are a subset of the internal angles in 6gons. Like the faces in Kepler's rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular. We show that there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle. Unlike carbon fullerenes and faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical. The reasoning and techniques presented here will enable discovery of still more classes of convex equilateral polyhedra with polyhedral symmetry.

Cryo-EM structure of the mature dengue virus at 3.5-Å resolution.

Regulated by pH, membrane-anchored proteins E and M function during dengue virus maturation and membrane fusion. Our atomic model of the whole virion from cryo-electron microscopy at 3.5-Å resolution reveals that in the mature virus at neutral extracellular pH, the N-terminal 20-amino-acid segment of M (involving three pH-sensing histidines) latches and thereby prevents spring-loaded E fusion protein from prematurely exposing its fusion peptide. This M latch is fastened at an earlier stage, during maturation at acidic pH in the trans-Golgi network. At a later stage, to initiate infection in response to acidic pH in the late endosome, M releases the latch and exposes the fusion peptide. Thus, M serves as a multistep chaperone of E to control the conformational changes accompanying maturation and infection. These pH-sensitive interactions could serve as targets for drug discovery.

Cone synapses in macaque fovea: I. Two types of non-S cones are distinguished by numbers of contacts with OFF midget bipolar cells.

L and M cones, divided into two groups by absorption spectra, have not been distinguished by structure. Here, we report what may be such a difference. We reconstructed the synaptic terminals of 16 non-S cones and the dendritic arbors of their ON and OFF midget bipolar cells from high-magnification electron micrographs of serial thin sections of a small region of macaque fovea. Each cone terminal contacted a similar number (~16) of invaginating central elements provided by its ON midget bipolar cell. By contrast, the numbers of connections between a cone terminal and its OFF midget bipolar cell were grouped into two clusters: 30-37 versus 43-50 basal contacts in the triad-associated position and 41-47 versus 61-74 Outer Densities within those basal contacts. The coefficients of variation of these distributions were all in the range of 10% or lower, characteristic of single populations. If these two clusters correspond to M- and L-cone circuits, the results reveal structural differences between M and L cones and between their corresponding OFF midget bipolar cells.

Cone synapses in macaque fovea: II. Dendrites of OFF midget bipolar cells exhibit Inner Densities similar to their Outer synaptic Densities in basal contacts with cone terminals.

As described in the companion paper, the synaptic terminal of a cone photoreceptor in macaque monkey makes an average of 35 or 46 basal contacts with the tips of the dendrites of its OFF midget bipolar cell. Each basal contact has one or more symmetrically thickened dense regions. These "Outer Densities," averaging 48 or 67 in number, harbor clusters of ionotropic glutamate receptors and are ~0.8 µm (and ~1-ms diffusion time) from active zones associated with synaptic ribbons. Here, we show similarly appearing "Inner Densities," averaging 53 or 74 in number, located more proximally on the dendrites of these OFF midget bipolar cells, ~0.4 µm inward from the tips of the dendrites and out of contact with the basal surface of the cone terminal. Compared to desmosome-like junctions, Inner Densities are closer to the terminal and are less dense and less thick. Each Inner Density is shared with another cell, the partners including diffuse bipolar cells, ON midget bipolar cells, and horizontal cells. Given the diversity of the partners, the OFF midget bipolar cells are unlikely to be in a synaptic relationship with the partners. Instead, Inner Densities are near enough to the active zones associated with synaptic ribbons to receive pulses of glutamate at concentrations effective for glutamate receptors. The role of Inner Densities is not known, but they might represent additional clusters of glutamate receptors.

Atomic structure of human adenovirus by cryo-EM reveals interactions among protein networks.

Construction of a complex virus may involve a hierarchy of assembly elements. Here, we report the structure of the whole human adenovirus virion at 3.6 angstroms resolution by cryo-electron microscopy (cryo-EM), revealing in situ atomic models of three minor capsid proteins (IIIa, VIII, and IX), extensions of the (penton base and hexon) major capsid proteins, and interactions within three protein-protein networks. One network is mediated by protein IIIa at the vertices, within group-of-six (GOS) tiles--a penton base and its five surrounding hexons. Another is mediated by ropes (protein IX) that lash hexons together to form group-of-nine (GON) tiles and bind GONs to GONs. The third, mediated by IIIa and VIII, binds each GOS to five surrounding GONs. Optimization of adenovirus for cancer and gene therapy could target these networks.

Bluetongue virus coat protein VP2 contains sialic acid-binding domains, and VP5 resembles enveloped virus fusion proteins.

Bluetongue virus (BTV) is transmitted by blood-feeding insects (Culicoides sp.) and causes hemorrhagic diseases in livestock. BTV is a nonenveloped, double-stranded RNA (dsRNA) virus with two capsids: a well-studied, stable core enclosing the dsRNA genome and a highly unstable, poorly studied coat responsible for host cell attachment and entry. Here, based on cryo-electron microscopy (cryoEM), we report a 7-A resolution structure of the infectious BTV virion, including the coat proteins. We show that unlike other dsRNA viruses, the VP2 attachment trimer has a triskelion shape composed of three tip domains branching from a central hub domain. We identify three putative sialic acid-binding pockets in the hub and present supporting biochemical data indicating sugar moiety binding is important for BTV infection. Despite being a nonenveloped virus, the putative VP5 membrane penetration trimer, located slightly inward of the VP2 attachment trimer, has a central coiled-coil alpha-helical bundle, similar to the fusion proteins of many enveloped viruses (e.g., HIV, herpesviruses, vesicular stomatitis virus, and influenza virus). Moreover, mapping of the amino acid sequence of VP5 to the secondary structural elements identified by cryoEM locates 15 amphipathic alpha-helical regions on the external surface of each VP5 trimer. The cryoEM density map also reveals few, weak interactions between the VP5 trimer and both the outer-coat VP2 trimer and the underlying core VP7 trimer, suggesting that the surface of VP5 could unfurl like an umbrella during penetration and shedding of the coat to release the transcriptionally active core particle.

Cryo-EM model of the bullet-shaped vesicular stomatitis virus.

Vesicular stomatitis virus (VSV) is a bullet-shaped rhabdovirus and a model system of negative-strand RNA viruses. Through direct visualization by means of cryo-electron microscopy, we show that each virion contains two nested, left-handed helices: an outer helix of matrix protein M and an inner helix of nucleoprotein N and RNA. M has a hub domain with four contact sites that link to neighboring M and N subunits, providing rigidity by clamping adjacent turns of the nucleocapsid. Side-by-side interactions between neighboring N subunits are critical for the nucleocapsid to form a bullet shape, and structure-based mutagenesis results support this description. Together, our data suggest a mechanism of VSV assembly in which the nucleocapsid spirals from the tip to become the helical trunk, both subsequently framed and rigidified by the M layer.

Architecture of clathrin fullerene cages reflects a geometric constraint--the head-to-tail exclusion rule--and a preference for asymmetry.

Fullerene cages have n trivalent vertices, 12 pentagonal faces, and (n-20)/2 hexagonal faces. The smallest cage in which all of the pentagons are surrounded by hexagons and thus isolated from each other has 60 vertices and is shaped like a soccer ball. The protein clathrin self-assembles into fullerene cages of a variety of sizes and shapes, including smaller ones with adjacent pentagons as well as larger ones, but the variety is limited. To explain the range of clathrin architecture and how these fullerene cages self-assemble, we proposed a hypothesis, the "head-to-tail exclusion rule" (the "Rule"). Of the 5769 small clathrin cage isomers with n< or =60 vertices and adjacent pentagons, the Rule permits just 15, three identified in 1976 and 12 others. A "weak version" of the Rule permits another 99. Based on cryo-electron tomography, Cheng et al. reported six raw clathrin fullerene cages. One was among the three identified in 1976. Here, (1) we identify the remaining five. (2) Four are new and are among the 12 others permitted by the Rule. (3) One, also new, is among the 99 weak version cages. (4) Of particular note, none of the remaining 5565 excluded cages has been identified. These findings provide powerful experimental confirmation of the Rule and the principle on which it is based. (5) Surprisingly, the newly identified clathrin cages are among the least symmetric of those permitted. (6) By devising a method for counting assembly paths, (7) we show that asymmetric cages can be assembled by larger numbers of paths, thus providing a kinetic explanation for the prevalence of asymmetric cages. (8) Finally, we show that operation during cage growth of the Rule greatly increases the likelihood of producing a closed fullerene cage, specifically one of those permitted, but efficient assembly still appears to require internal remodeling.

A geometric constraint, the head-to-tail exclusion rule, may be the basis for the isolated-pentagon rule in fullerenes with more than 60 vertices.

Carbon atoms self-assemble into the famous soccer-ball shaped Buckminsterfullerene (C(60)), the smallest fullerene cage that obeys the isolated-pentagon rule (IPR). Carbon atoms self-assemble into larger (n > 60 vertices) empty cages as well-but only the few that obey the IPR-and at least 1 small fullerene (n 60, the head-to-tail exclusion rule permits only (and all) fullerene cages and nanotubes that obey the IPR. We therefore suggest that self-assembly that obeys the IPR may be explained by the head-to-tail exclusion rule, a geometric constraint.

The physical basis for the head-to-tail rule that excludes most fullerene cages from self-assembly.

In the companion article, we proposed that fullerene cages with head-to-tail dihedral angle discrepancies do not self-assemble. Here we show why. If an edge abuts a pentagon at one end and a hexagon at the other, the dihedral angle about the edge increases, producing a dihedral angle discrepancy (DAD) vector. The DADs about all five/six edges of a central pentagonal/hexagonal face are determined by the identities-pentagon or hexagon-of its five/six surrounding faces. Each "Ring"-central face plus specific surrounding faces-may have zero, two, or four edges with DAD. In most Rings, the nonplanarity induced by DADs is shared among surrounding faces. However, in a Ring that has DADs arranged head of one to tail of another, the nonplanarity cannot be shared, so some surrounding faces would be especially nonplanar. Because the head-to-tail exclusion rule is an implicit geometric constraint, the rule may operate either by imposing a kinetic barrier that prevents assembly of certain Rings or by imposing an energy cost that makes those Rings unlikely to last in an equilibrium circumstance. Since Rings with head-to-tail DADs would be unlikely to self-assemble or last, fullerene cages with those Rings would be unlikely to self-assemble.

A geometric principle may guide self-assembly of fullerene cages from clathrin triskelia and from carbon atoms.

Clathrin triskelia and carbon atoms alike self-assemble into a limited selection of fullerene cages (with n three connected vertices, 3n/2 edges, 12 pentagonal faces, and (n-20)/2 hexagonal faces). We show that a geometric constraint-exclusion of head-to-tail dihedral angle discrepancies (DADs)-explains this limited selection as well as successful assembly into such closed cages in the first place. An edge running from a pentagon to a hexagon has a DAD, since the dihedral angles about the edge broaden from its pentagon (tail) end to its hexagon (head) end. Of the 21 configurations of a central face and surrounding faces, six have such DAD vectors arranged head-to-tail. Of the 5770 mathematically possible fullerene cages for n

Efficiency of synaptic transmission of single-photon events from rod photoreceptor to rod bipolar dendrite.

A rod transmits absorption of a single photon by what appears to be a small reduction in the small number of quanta of neurotransmitter (Q(count)) that it releases within the integration period ( approximately 0.1 s) of a rod bipolar dendrite. Due to the quantal and stochastic nature of release, discrete distributions of Q(count) for darkness versus one isomerization of rhodopsin (R*) overlap. We suggested that release must be regular to narrow these distributions, reduce overlap, reduce the rate of false positives, and increase transmission efficiency (the fraction of R* events that are identified as light). Unsurprisingly, higher quantal release rates (Q(rates)) yield higher efficiencies. Focusing here on the effect of small changes in Q(rate), we find that a slightly higher Q(rate) yields greatly reduced efficiency, due to a necessarily fixed quantal-count threshold. To stabilize efficiency in the face of drift in Q(rate), the dendrite needs to regulate the biochemical realization of its quantal-count threshold with respect to its Q(count). These considerations reveal the mathematical role of calcium-based negative feedback and suggest a helpful role for spontaneous R*. In addition, to stabilize efficiency in the face of drift in degree of regularity, efficiency should be approximately 50%, similar to measurements.

A clockwork hypothesis: synaptic release by rod photoreceptors must be regular.

We can see at light intensities much lower than an average of one photon per rod photoreceptor, demonstrating that rods must be able to transmit a signal after absorption of a single photon. However, activation of one rhodopsin molecule (Rh*) hyperpolarizes a mammalian rod by just 1 mV. Based on the properties of the voltage-dependent Ca2+ channel and data on [Ca2+] in the rod synaptic terminal, the 1 mV hyperpolarization should reduce the rate of release of quanta of neurotransmitter by only 20%. If quantal release were Poisson, the distributions of quantal count in the dark and in response to one Rh* would overlap greatly. Depending on the threshold quantal count, the overlap would generate too frequent false positives in the dark, too few true positives in response to one Rh*, or both. Therefore, quantal release must be regular, giving narrower distributions of quantal count that overlap less. We model regular release as an Erlang process, essentially a mechanism that counts many Poisson events before release of a quantum of neurotransmitter. The combination of appropriately narrow distributions of quantal count and a suitable threshold can give few false positives and appropriate (e.g., 35%) efficiency for one Rh*.

Evidence that each S cone in macaque fovea drives one narrow-field and several wide-field blue-yellow ganglion cells.

A rule of retinal wiring is that many receptors converge onto fewer bipolar cells and still fewer ganglion cells. However, for each S cone in macaque fovea, there are two S-cone ON bipolar cells and two blue-yellow (BY) ganglion cells. To understand this apparent rule reversal, we reconstructed synaptic patterns of divergence and convergence and determined the basic three-tiered unit of connectivity that repeats across the retina. Each foveal S cone diverges to four S-cone ON bipolar cells but contacts them unequally, providing 1-16 ribbon synapses per cell. Next, each bipolar cell diverges to two BY ganglion cells and also contacts them unequally, providing approximately 14 and approximately 28 ribbon synapses per cell. Overall, each S cone diverges to approximately six BY ganglion cells, dominating one and contributing more modestly to the others. Conversely, of each pair of BY ganglion cells, one is dominated by a single S cone and one is diffusely driven by several. This repeating circuit extracts blue/yellow information on two different spatiotemporal scales and thus parallels the circuits for achromatic, spatial vision, in which each cone dominates one narrow-field ganglion cell (midget) and contributes some input to several wider-field ganglion cells (parasol). Finally, because BY ganglion cells have coextensive +S and -(L+M) receptive fields, and each S cone contributes different weights to different BY ganglion cells, the coextensive receptive fields must be already present in the synaptic terminal of the S cone. The S-cone terminal thus constitutes the first critical locus for BY color vision.