A Geometric Principle May Guide Self-Assembly of Fullerene Cages from Clathrin Triskelia and from Carbon Atoms (original) (raw)
Related papers
The Physical Basis for the Head-to-Tail Rule that Excludes Most Fullerene Cages from Self-Assembly
Biophysical Journal, 2008
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-totail 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.
Proceedings of the National Academy of Sciences, 2008
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) with adjacent pentagons. Clathrin protein also self-assembles into small fullerene cages with adjacent pentagons, but just a few of those. We asked why carbon atoms and clathrin proteins self-assembled into just those IPR and small cage isomers. In answer, we described a geometric constraint-the head-to-tail exclusion rule-that permits self-assembly of just the following fullerene cages: among the 5,769 possible small cages (n < 60 vertices) with adjacent pentagons, only 15; the soccer ball (n ؍ 60); and among the 216,739 large cages with 60 < n < 84 vertices, only the 50 IPR ones. The last finding was a complete surprise. Here, by showing that the largest permitted fullerene with adjacent pentagons is one with 60 vertices and a ring of interleaved hexagons and pentagon pairs, we prove that for all 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.
Journal of Molecular Biology, 2009
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 ≤ 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.
Protein-directed self-assembly of a fullerene crystal
Nature communications, 2016
Learning to engineer self-assembly would enable the precise organization of molecules by design to create matter with tailored properties. Here we demonstrate that proteins can direct the self-assembly of buckminsterfullerene (C60) into ordered superstructures. A previously engineered tetrameric helical bundle binds C60 in solution, rendering it water soluble. Two tetramers associate with one C60, promoting further organization revealed in a 1.67-Å crystal structure. Fullerene groups occupy periodic lattice sites, sandwiched between two Tyr residues from adjacent tetramers. Strikingly, the assembly exhibits high charge conductance, whereas both the protein-alone crystal and amorphous C60 are electrically insulating. The affinity of C60 for its crystal-binding site is estimated to be in the nanomolar range, with lattices of known protein crystals geometrically compatible with incorporating the motif. Taken together, these findings suggest a new means of organizing fullerene molecules...
Constructing Molecules with Beads: The Geometry of Topologically Nontrivial Fullerenes
Three-dimensional molecular structures of topologically nontrivial fullerenes (consisting of either finite or extended structures) are usually aesthetically pleasing. In this article, we demonstrate that beads such as the ones commonly used in decorative art and ornament making can also be used to construct arbitrary fullerene structures. Based on the spiral codes of fullerenes, we developed a systematic strategy for making physical models of cage-like fullerenes use common beads. The resulting beaded model structure is similar to the true three-dimensional molecular structure of corresponding fullerene due to an interesting analogy between the hard-sphere repulsion among neighboring beads and the microscopic valence shell electron pair repulsion for the sp 2-hybridized carbon atoms. More complicated fullerenes models that have nontrivial topology (e.g. toroidal carbon nanotubes, helically coiled carbon nanotubes, and high-genus fullerenes) can also be faithfully constructed using beads. Beaded models of extended graphitic structures such as those that correspond to tiling of graphene sheet on a Schwartz P-and Dsurfaces, Shoen I-WP, and Nervious surfaces, can also been created.
Playing with Hexagons and Pentagons: Topological and Graph Theoretical Aspects of Fullerenes
Regular fullerenes are cubic planar connected graphs consisting of pentagons and hexagons only and come in many different shapes. There has been great progress over the last two decades describing the topological and graph theoretical properties of fullerenes, but leaving still many unsolved and interesting mathematical and chemical problems open in this field. For example, i) how to generate all possible fullerene isomers for a fixed atom count (where an efficient algorithm was introduced only very recently) ii) are fullerenes Hamiltonian (Barnette's conjecture) and what is the number of distinct Hamiltonian cycles (longest carbon chains), iii) the Pauling bond order and the number of different Kekulé structures (perfect matchings), iv) the search for suitable topological (chemical) indices to find the most stable fullerene structure out of the many (∼ N 9 ) possibilities, or how to pack fullerenes in 3D space (the Hilbert problem) to name but a few. Here we present a general overview on recent topological and graph theoretical developments in fullerene research over the past two decades.
A Modeling Study of the Self-Assembly of Various Hydrogen-Bonding Fullerene Derivatives on Au(111)
The Journal of Physical Chemistry C, 2010
Several experimental groups have recently reported self-assembly of fullerene derivatives on metal substrates. These studies have shown that both the size of the substituent moiety and the presence of hydrogen-bonding functional groups affect the observed adlayer symmetries. However, little theoretical work has been carried out to explain these results. Accordingly, we have carried out classical rigid body Monte Carlo simulations of a variety of fullerene derivatives on a rigid Au(111) surface. We consider several fullerene derivatives functionalized with carboxylic acid groups attached to the fullerene using "arms" of phenyl rings of variable length. A pairwise-additive united-atom potential energy function was constructed using data from a variety of sources. The potential reproduces many of the details observed in experimental studies of C 60 on Au(111). For fullerenes containing two hydrogen-bonding groups, ordered rows of molecules can self-assemble if the fullerenes are able to form a close-packed layer. Steric effects may inhibit close-packing of the fullerenes, resulting in "glassy" adlayers. In addition, the rotational barriers must be sufficiently low that they allow orientational ordering of the molecular adlayer. We have identified two distinct adlayer geometries which can be formed from extended one-dimensional hydrogen-bonding rows. When the barriers to rotation are too high, as is the case when the molecules become sterically hindered, orientational ordering is not possible. Simulations with molecules bearing a single carboxylic acid functionality lead to close-packing and hydrogenbonded orientational dimers. However, the dimers do not self-assemble into a globally ordered adlayer (with the parametrization used here). In addition, we show that molecules without hydrogen-bonding functional groups can self-assemble into herringbone patterns, provided the conditions for close-packing and orientational ordering have been met. Our findings rationalize several of the experimental results in the literature.
Self-organisation of fullerene-containing conical supermesogens
Soft Matter, 2008
A molecular model of cubic building blocks is used to describe the mesomorphism of conical fullerenomesogens. Calculations based on density functional molecular theory and on Monte Carlo computer simulations give qualitatively similar results that are also in good agreement with the experimentally observed mesomorphic behaviour. The columnar and lamellar mesophases obtained are non-polar, and their relative stability is controlled by a single model parameter representing the softness of the repulsive interactions among the building blocks of the conical molecules.
Assembly of Fullerene Fine Crystals: Fabrication of 1D, 2D and 3D Structures from 0D Fullerene
2022
Fullerene molecules with closed cage structures, extended π systems, excellent mechanical and photochemical stability and unique semiconducting properties are ideal blocks to construct various supramolecular assemblies and functional materials. Furthermore, zero- dimensional fullerene molecules with only a single elemental component, carbon, without any charged or interactive functional groups are excellent units for self assembly. Researches on fullerene micro and nanostructures, especially crystallization of fullerene molecules into ordered molecular assemblies have grown rapidly during recent years. In this short review, we introduce various examples of self assembled fullerenes and their derivatives. An outline and background of fullerene properties are first described (introduced), followed by several examples of fullerene assemblies, such as wiskers, tubes, sheets, cubes, hole in cubes and hopper shaped fullerenes. Also a demonstration of factors influencing morphologies of fu...