FIG 1 - uploaded by Juergen Brosius
Content may be subject to copyright.
Amino-terminal amino acid sequence determination and design of oligonucleotide probe. (Left) Bovine clathrin (heavy and
Source publication
We have deduced the 1675-amino acid sequence of rat clathrin heavy chain from cDNA clones and predict a protein of Mr 191,569. We have established the polarity of the heavy chain and assigned sequence positions to several structural landmarks of the clathrin leg. The terminal domain at the distal end of the clathrin leg is at the amino terminus of...
Contexts in source publication
Context 1
... Isolation. A XgtlO rat brain cytoplasmic poly(A)+ cDNA library (20) was screened with a unique-sequence 122-base-pair DNA probe ( Fig. 1 Right) as described (22). Additional clones were isolated from XgtlO cDNA libraries constructed from rat liver cytoplasmic poly(A)+ RNA, from bovine brain poly(A)+ RNA (20), and from a plasmid cDNA tTo whom reprint requests should be addressed. 1This sequence is being deposited in the EMBL/GenBank data base (Bolt, Beranek, and Newman ...
Context 2
... Thus, to obtain internal amino acid sequence information, peptides from bovine clathrin were generated by partial cleavage with CNBr. A Mr -23,000 fragment yielded a sequence of 51 amino acids (peptide 1, Figs. 1 Left and 2) from which we selected a region of 41 consecutive amino acids to design a probe spanning 122 nucleotides of unique sequence (Fig. 1 Right). Six independent and related hybridizing clones were identified after initial screening of a XgtlO library from rat brain. The deduced amino acid sequence ofthe smallest clone confirmed its identity as a partial clathrin heavy-chain cDNA. The agreement included the complete amino acid sequence of peptide 1 as well as 26 out of ...
Similar publications
Many receptors involved with innate immunity activate the inhibitor kappa B kinase signalosome (IKK). The active complex appears to be assembled from the two kinase units, IKKα and IKKβ with the regulatory protein NEMO. Because we previously found that RNA silencing of clathrin heavy chains (CHC), in transformed human lung pneumocytes (A549), decre...
Congenital inability to feel pain is very rare but the identification of causative genes has yielded significant insights into pain pathways and also novel targets for pain treatment. We report a novel recessive disorder characterized by congenital insensitivity to pain, inability to feel touch, and cognitive delay. Affected individuals harboured a...
The symbiotic association between the legume Lotus japonicus and the nitrogen-fixing bacterium Mesorhizobium loti results in the formation of root nodules. This process begins with the recognition of the rhizobial nodulation factor (NF) by the NF receptors (NFR) at the cell surface of the host roots. The downstream signaling cascades after NFR reco...
Citations
... The major vertebrate clathrin, responsible for receptor-mediated endocytosis and other housekeeping membrane traffic pathways, is formed from clathrin heavy chain CHC17 (herein referred to as CHC) associated with clathrin light chains (CLCs), which do not bind the minor CHC22 clathrin isoform 5 , which mediates specialised trafficking in muscle cells. Vertebrate CLCs are encoded by two different genes CLTA and CLTB, producing CLCa and CLCb isoforms of about 60% sequence identity 6,7 . ...
... Their sequence differences have been conserved throughout evolution after their encoding genes arose through duplication, suggesting the two isoforms can mediate distinct functions 8,9 . Expression levels of the CLCa and CLCb isoforms are tissue-specific 10 , and further variation is created by alternative gene splicing during development 11 and in brain 6,7 . Here we address how CLC diversity affects the biophysical properties of clathrin and how the resulting variation affects the specialised function of clathrin in SV recycling. ...
Clathrin light chain (CLC) subunits in vertebrates are encoded by paralogous genes CLTA and CLTB and both gene products are alternatively spliced in neurons. To understand how this CLC diversity influences neuronal clathrin function, we characterised the biophysical properties of clathrin comprising individual CLC variants for correlation with neuronal phenotypes of mice lacking either CLC-encoding gene. CLC splice variants differentially influenced clathrin knee conformation within assemblies, and clathrin with neuronal CLC mixtures was more effective in membrane deformation than clathrin with single neuronal isoforms nCLCa or nCLCb. Correspondingly, electrophysiological recordings revealed that neurons from mice lacking nCLCa or nCLCb were both defective in synaptic vesicle replenishment. Mice with only nCLCb had a reduced synaptic vesicle pool and impaired neurotransmission compared to wild-type mice, while nCLCa-only mice had increased synaptic vesicle numbers, restoring normal neurotransmission. These findings highlight differences between the CLC isoforms and show that isoform mixing influences tissue-specific clathrin activity in neurons, which requires their functional balance.
SIGNIFICANCE STATEMENT
This study reveals that diversity of clathrin light chain (CLC) subunits alters clathrin properties and demonstrates that the two neuronal CLC subunits work together for optimal clathrin function in synaptic vesicle formation. Our findings establish a role for CLC diversity in synaptic transmission and illustrate how CLC variability expands the complexity of clathrin to serve tissue-specific functions.
... The absence of a discernible electron dense coat impeded the characterization of this CIE pathway or pathways, and they are still being discovered, with Endophilin A-dependent FEME being the most recent addition to CIE (2015). Important milestones in the discovery of multiple endocytic pathways are as follows: a, Palade 1953, Yamada 1955b, Roth & Porter 1964;c, Pearse 1975c, Pearse , 1976d, Anderson et al. 1977a,b;e, Bretscher et al. 1980;f, Kosaka & Ikeda 1983;g, Moya et al. 1985, Sandvig 1987h, Bar-Sagi & Feramisco 1986;i, Jackson et al. 1987, Kirchhausen et al. 1987aj, Robinson 1989, Thurieau et al. 1988k, Rothberg et al. 1992, Tang et al. 1996l, Damke et al. 1994;m, Damke et al. 1994m, Damke et al. , 1995n, Radhakrishna & Donaldson 1997;o, Lamaze et al. 2001;p, Sabharanjak et al. 2002;q, Aboulaich et al. 2004, Hill et al. 2008r, Frick et al. 2007, Glebov et al. 2006s, Gupta et al. 2009, Kumari & Mayor 2008t, Boucrot et al. 2015, Renard et al. 2015u, Sathe et al. 2018. Abbreviations: ARF1, ADP-ribosylation factor 1; CG, CLIC (clathrin-independent carrier)/GEEC (glycosylphosphatidylinositol-anchored protein-enriched compartment); CIE, clathrin-independent endocytosis; CME, clathrin-mediated endocytosis; FEME, fast endophilin A-mediated endocytosis; GBF1, Golgi-specific brefeldin A resistance factor 1; GEF, guanine nucleotide exchange factor; GPI-AP, glycosylphosphatidylinositol-anchored protein; I-BAR, inverse-BAR; IL2R, interleukin-2 receptor. ...
Endocytosis has long been identified as a key cellular process involved in bringing in nutrients, in clearing cellular debris in tissue, in the regulation of signaling, and in maintaining cell membrane compositional homeostasis. While clathrin-mediated endocytosis has been most extensively studied, a number of clathrin-independent endocytic pathways are continuing to be delineated. Here we provide a current survey of the different types of endocytic pathways available at the cell surface and discuss a new classification and plausible molecular mechanisms for some of the less characterized pathways. Along with an evolutionary perspective of the origins of some of these pathways, we provide an appreciation of the distinct roles that these pathways play in various aspects of cellular physiology, including the control of signaling and membrane tension.
Expected final online publication date for the Annual Review of Cell and Developmental Biology Volume 35 is October 7, 2019. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
... Only when the CLC is retracted from the knee segment of CHC (second conformation), either by downregulating the pH (< 6.5), or by interacting with adaptors at physiological pH, the clathrin lattice can assemble. When assembled, each leg of a triskelion protrudes towards the center of the cage or vesicle to interact with adaptors via the terminal domain (Vigers et al., 1986, Kirchhausen et al., 1987, ter Haar et al., 1998, Ybe et al., 1999, Fotin et al., 2004, Knuehl et al., 2006, Ybe et al., 2007, Wilbur et al., 2010. ...
Receptor-mediated endocytosis by clathrin coated vesicles (CCVs) is a well investigated process, in which clathrin, the adaptor AP-2 and the large GTPase dynamin play crucial roles. However, the minimal machinery for the formation of CCVs has not been defined in vitro. Specifically, scission of clathrin coated endocytic buds (CCBs), the last step in this process that results in the release of free vesicles, is not clearly defined mechanistically. Actually, five APcomplexes are described and except AP-2, all are recruited in an Arf-dependent manner to their donor membrane. Here, Arf is likely to play a distinct and GTPase activity-independent role in the scission mechanism via its myristoylated amphipathic helix, as has been shown for Arf’s role in COPI vesicle scission. In case of AP-2 no Arf is known to be involved, but it has been shown that epsin-1 with its N-terminal amphiphilic helix (ENTH-domain) is an endocytic accessory protein involved in the biogenesis of endocytic clathrin coated vesicles and was suggested to be implicated in scission. To identify the minimal machinery required for CCV formation and to investigate the molecular roles of dynamin and epsin-1 in this process, an in vitro reconstitution system for the biogenesis of CCVs was established using defined components in the form of synthetic membranes and recombinant, purified proteins. I observed that a combination of AP-2 and epsin-1 recruits clathrin to synthetic liposomes more efficiently than each single adaptor, indicating cooperativity between AP-2 and epsin-1. CCVreconstitution experiments with giant unilamellar vesicles showed that clathrin coated vesicles can be reconstituted dependent on clathrin adaptors, clathrin, dynamin and GTP. Moreover, blocking GTP-hydrolysis abolished the formation of CCVs, supporting the widely accepted hypothesis that hydrolysis of GTP by dynamin is mandatory for vesicle release. However, as hydrolysis of GTP was an absolute requirement of vesicle release, epsin-1 alone does not have the propensity for scission, but is required for bud formation, as AP-2 and clathrin alone are not sufficient. A role of the endocytic protein epsin-1 for the progression of endocytosis to CCBs would also be structurally supported as epsin-1 contains a membrane bending ENTH-domain that would facilitate such a function by introducing curvature to the membrane. In summary this work comprises the first in vitro reconstitution system of endocytic CCVs that uses full length proteins in a chemically defined environment. Using this system, I confirmed and refined the roles of known constituents of the minimal endocytic CCV biogenesis machinery, which is comprised of AP-2, epsin-1, clathrin, dynamin, and by GTP-hydrolysis in dynamin.
... Clathrin heavy chain (CHC/Chc) is the major structural protein of coated vesicles, the principal organelles of receptor-mediated endocytosis in mammals (Pearse, 1975(Pearse, , 1976. Characterization of cDNA encoding CHC/Chc has been characterized mainly in mammals (Kirchhausen et al., 1987;Dodge et al., 1991;Liu et al., 1995), insects (Bazinet et al., 1993;, and yeast (Payne and Schekman, 1985;Lemmon and Jones, 1987;Silveria et al., 1990;Lemmon et al., 1991). In vertebrates, including teleost fishes, two isoforms of CHC (termed CLTC and CLTD), which are encoded by separate genes, were evident (Wakeham et al., 2005). ...
... In vertebrates, there are two isoforms of clathrin heavy chain (Cltc/ CLTC and Cltd/CLTD). The vertebrate Cltc/CLTC and invertebrate Chc have been identified in a number of species such as several mammals (Kirchhausen et al., 1987;Dodge et al., 1991;Liu et al., 1995), mosquito , fruit fly (Bazinet et al., 1993), yeast (Lemmon et al., 1991), and slime mold (O'Halloran and Anderson, 1992). Duality of chc transcripts has been confirmed in mosquito; two isoforms that differ at the very beginning of the N-terminal domain, ovary-specific chc-a and somatic-specific chc-b, have been identified . ...
... Quantification of mRNA by rtqRT-PCR revealed that the three types of cutthroat trout cltc are ubiquitously expressed in various tissues, with relatively high expression of cltc-a1 and cltc-a2 in intestine and predominant cltc-b expression in brain. In mammals, Cltc/CLTC is expressed in brain, heart, kidney, liver, lung, and testis, but does not have a predominant expression site (Kirchhausen et al., 1987;Dodge et al., 1991). Since clathrin is involved in the uptake of diverse ligands by receptor-mediated endocytosis (e.g., hormones, growth factors, and transport molecules such as transferrin and lipoproteins), the wide distribution of cltc transcripts in somatic and gonadal tissues is reasonable. ...
To evaluate potential involvement of clathrin in endocytosis of vitellogenin (Vtg) by teleost oocytes, cDNAs encoding clathrin heavy chain (cltc) were cloned from ovaries of cutthroat trout. Quantitative PCR revealed three types of cltc (cltc-a1, cltc-a2, cltc-b) to be expressed in 10 different tissues including the ovary. The cltc-a1 alone exhibited a significant decrease in ovarian expression during vitellogenesis; this was correlated with a corresponding decrease in transcripts encoding the major Vtg receptor (Vtgr). No development-related changes in ovarian cltc-a2 or cltc-b transcript levels were observed. In situ hybridization revealed a strong ctlc signal in pre-vitellogenic oocytes, but not in vitellogenic oocytes. Western blotting using a rabbit antiserum (a-Cltc) raised against a recombinant Cltc preparation detected a polypeptide band with an apparent mass of ~ 170 kDa in vitellogenic ovary extracts. Immunohistochemistry using a-Cltc revealed Cltc to be uniformly distributed throughout the ooplasm of perinucleolus stage oocytes, translocated to the periphery of lipid droplet stage oocytes, and localized to the oolemma during vitellogenesis. These patterns of cltc/Cltc distribution and abundance during oogenesis, which are identical to those previously reported for vtgr/Vtgr in this species, constitute the first empirical evidence that cltc-a1/Cltc-a1 is involved in Vtg endocytosis via the Vtgr in teleost fish.
... Since yeast Chc1 trimerization and stability requires binding to Clc1 (23,24), whereas mammalian CHC trimerizes independently of the clathrin LC (11,12,21,22), we tested whether mammalian heavy chain could function in yeast and override CHC instability in yeast lacking the clathrin light chain. However, due to difficulties with expression of full length rat CHC in yeast (data not shown), we instead created a novel allele encoding a fusion protein combining the N-terminal two-thirds of yeast CHC with the C-terminus from rat CHC, taking advantage of a conserved SacI restriction site in the coding sequences (33,34). This new engineered gene (CHC-YR) encoded the TD, distal leg, knee and initial residues of the proximal leg of the Yeast CHC (amino acids 1-1312) fused in frame with the remainder of the Rat CHC (amino acids 1318-1673) including the proximal leg, CLC binding region, the trimerization domain and the HSC70 binding site important for auxilin-dependent uncoating ( Figure 1A; 35). ...
Clathrin facilitates vesicle formation during endocytosis and sorting in the trans-Golgi network (TGN)/endosomal system. Unlike in mammals, yeast clathrin function requires both the heavy (CHC) and light (CLC) chain, since Chc1 does not form stable trimers without Clc1. To further delineate clathrin subunit functions, we constructed a chimeric CHC protein (Chc-YR), which fused the N-terminus of yeast CHC (1-1312) to the rat CHC residues 1318-1675, including the CHC trimerization region. The novel CHC-YR allele encoded a stable protein that fractionated as a trimer. Chc-YR also complemented chc1∆ slow growth and clathrin TGN/endosomal sorting defects. In strains depleted for Clc1 (either clc1∆ or chc1∆ clc1∆), CHC-YR, but not CHC1, suppressed TGN/endosomal sorting and growth phenotypes. Chc-YR-GFP localized to the TGN and cortical patches on the plasma membrane, like Chc1 and Clc1. However, Clc1-GFP was primarily cytoplasmic in chc1∆ cells harboring pCHC-YR, indicating that Chc-YR does not bind yeast CLC. Still, some partial phenotypes persisted in cells with Chc-YR, which are likely due either to loss of CLC recruitment or chimeric HC lattice instability. Ultimately, these studies have created a tool to examine non-trimerization roles for the clathrin LC.
... The problem was not getting enough protein (12 bovine brains routinely yield >100 mg of purified clathrin), but getting the protein to crystallize. Finally Tommy Kirchhausen's lab tried using recombinant clathrin heavy chain, which they had cloned and sequenced in 1987 (23), and succeeded in crystallizing the first 494 residues, which comprise the foot and part of the ankle of a single triskelion leg (17). Unexpectedly, because this was not predicted from the sequence, residues 1-330 were found to form a seven-bladed β-propeller, followed by 10 short α helices stacked against each other A B ...
The purification of coated vesicles and the discovery of clathrin by Barbara Pearse in 1975 was a landmark in cell biology. Over the past 40 years, work from many labs has uncoveredthe molecular details of clathrin and its associated proteins, including how they assemble into a coated vesicle and how they select cargo. Unexpected connections have been found with signalling, development, neuronal transmission, infection, immunity, and genetic disorders. But there are still a number of unanswered questions, including how clathrin-mediated trafficking is regulated and how the machinery evolved.
... The clathrin-H-link domain is short and often appears directly downstream from the clathrin heavy-chain linker [22]. Clathrin and VPS repeat regions are approximately 140 amino acids long, composed of multiple alpha helical repeats and occur in the arm regions of the clathrin heavy chain [23,24], as well as in VPS proteins [25]. ...
Background
Clathrin-mediated vesicular trafficking, the mechanism by which proteins and lipids are transported between membrane-bound organelles, accounts for a large proportion of import from the plasma membrane (endocytosis) and transport from the trans-Golgi network towards the endosomal system. Clathrin-mediated events are still poorly understood in the protozoan Trypanosoma cruzi, the causative agent of Chagas disease in Latin America. In this study, clathrin heavy (TcCHC) and light (TcCLC) chain gene expression and protein localization were investigated in different developmental forms of T. cruzi (epimastigotes, trypomastigotes and amastigotes), using both polyclonal and monoclonal antibodies raised against T. cruzi recombinant proteins.
Results
Analysis by confocal microscopy revealed an accumulation of TcCHC and TcCLC at the cell anterior, where the flagellar pocket and Golgi complex are located. TcCLC partially colocalized with the Golgi marker TcRAB7-GFP and with ingested albumin, but did not colocalize with transferrin, a protein mostly ingested via uncoated vesicles at the cytostome/cytopharynx complex.
Conclusion
Clathrin heavy and light chains are expressed in T. cruzi. Both proteins typically localize anterior to the kinetoplast, at the flagellar pocket and Golgi complex region. Our data also indicate that in T. cruzi epimastigotes clathrin-mediated endocytosis of albumin occurs at the flagellar pocket, while clathrin-independent endocytosis of transferrin occurs at the cytostome/cytopharynx complex.
... Up until now, the genes encoding clathrin heavy chain have only been well characterized in rat [17], yeast [18], human [19,20], Drosophila [21,22], soybean [12], pig [23], and Arabidopsis [11]. Multiple sequence alignments of the deduced amino acids of ZmCHC1 and ZmCHC2 showed that ZmCHC1 and ZmCHC2 shared 96.1% sequence identity with each other, and that ZmCHC1 shared 90.3%, 89.9%, and 88.9% sequence identity with Arabidopsis AtCHC1, AtCHC2, and soybean GmCHC, respectively. ...
... The flexible linker, light chain binding and trimerization domains of ZmCHC1 and ZmCHC2 are highly conserved to those domains in CHCs characterized in only two other plants (Figure 2), soybean [12] and Arabidopsis [11]. The flexible linker (residues 479-523 in rat CHC), also found in both of ZmCHC1 and ZmCHC2 (Figure 2), allows the globular N-terminal domain to project inwards and make contact with the adaptor complex [17]. The weakly predicted pattern of heptad repeats spanning residues 1107-1184 in rat CHC [17] or residues 1120-1197 in soybean GmCHC [12], aligns to the residues 1112-1189 in ZmCHC1 or residues 1157-1234 in ZmCHC2 (Figure 2). ...
... The flexible linker (residues 479-523 in rat CHC), also found in both of ZmCHC1 and ZmCHC2 (Figure 2), allows the globular N-terminal domain to project inwards and make contact with the adaptor complex [17]. The weakly predicted pattern of heptad repeats spanning residues 1107-1184 in rat CHC [17] or residues 1120-1197 in soybean GmCHC [12], aligns to the residues 1112-1189 in ZmCHC1 or residues 1157-1234 in ZmCHC2 (Figure 2). Two sequence domains of great structural importance in CHC proteins are the trimerization domain and the light chain binding domain. ...
Clathrin, a three-legged triskelion composed of three clathrin heavy chains (CHCs) and three light chains (CLCs), plays a critical role in clathrin-mediated endocytosis (CME) in eukaryotic cells. In this study, the genes ZmCHC1 and ZmCHC2 encoding clathrin heavy chain in maize were cloned and characterized for the first time in monocots. ZmCHC1 encodes a 1693-amino acid-protein including 29 exons and 28 introns, and ZmCHC2 encodes a 1746-amino acid-protein including 28 exons and 27 introns. The high similarities of gene structure, protein sequences and 3D models among ZmCHC1, and Arabidopsis AtCHC1 and AtCHC2 suggest their similar functions in CME. ZmCHC1 gene is predominantly expressed in maize roots instead of ubiquitous expression of ZmCHC2. Consistent with a typical predicted salicylic acid (SA)-responsive element and four predicted ABA-responsive elements (ABREs) in the promoter sequence of ZmCHC1, the expression of ZmCHC1 instead of ZmCHC2 in maize roots is significantly up-regulated by SA or ABA, suggesting that ZmCHC1 gene may be involved in the SA signaling pathway in maize defense responses. The expressions of ZmCHC1 and ZmCHC2 genes in maize are down-regulated by azide or cold treatment, further revealing the energy requirement of CME and suggesting that CME in plants is sensitive to low temperatures.
... A cDNA encoding rat clathrin heavy chain (Kirchhausen et al., 1987a) was used as a template to generate full-length (1675 HC), nested C-terminal truncations (1661 HC, 1643 HC, 1637 HC, 1630 HC, and 1596 HC), internal deletions (1675⌬ PIVYGQ HC, 1643⌬ PIVYGQ HC, and 1675⌬ QLMLTA HC), and mutations (1643 LML-AAA HC) of the heavy chain; each was then subcloned into the insect cell expression vector pFastBac1 (Invitrogen, Carlsbad, CA). A cDNA encoding rat liver clathrin light chain LCa (Kirchhausen et al., 1987b) was used as the template to subclone the region encoding the full light chain (residues 1-256) into the insect cell expression vector pFastBacHTb. ...
The 70-kDa heat-shock cognate protein (Hsc70) chaperone is an ATP-dependent "disassembly enzyme" for many subcellular structures, including clathrin-coated vesicles where it functions as an uncoating ATPase. Hsc70, and its cochaperone auxilin together catalyze coat disassembly. Like other members of the Hsp70 chaperone family, it is thought that ATP-bound Hsc70 recognizes the clathrin triskelion through an unfolded exposed hydrophobic segment. The best candidate is the unstructured C terminus (residues 1631-1675) of the heavy chain at the foot of the tripod below the hub, containing the sequence motif QLMLT, closely related to the sequence bound preferentially by the substrate groove of Hsc70 (Fotin et al., 2004b). To test this hypothesis, we generated in insect cells recombinant mammalian triskelions that in vitro form clathrin cages and clathrin/AP-2 coats exactly like those assembled from native clathrin. We show that coats assembled from recombinant clathrin are good substrates for ATP- and auxilin-dependent, Hsc70-catalyzed uncoating. Finally, we show that this uncoating reaction proceeds normally when the coats contain recombinant heavy chains truncated C-terminal to the QLMLT motif, but very inefficiently when the motif is absent. Thus, the QLMLT motif is required for Hsc-70-facilitated uncoating, consistent with the proposal that this sequence is a specific target of the chaperone.
... Such cages have n three-connected vertices, 3/2n edges, 12 pentagonal faces, and (n À 20)/2 hexagonal faces. Moreover, both carbon atoms, each just 12 Daltons, and clathrin trimers (triskelia) (6)(7)(8), each with mass ;50,000 times as much (6)(7)(8)(9)(10)(11), selfassemble into fullerene cages of a variety of sizes and shapes (2)(3)(4)(5)12,13). Carbon does this from the gas phase at temperatures around 1200°C (14)(15)(16). ...
... (A) The order for spiral addition of faces for cage 36-15 is 55656665556555566565, where ''5'' specifies a pentagon and ''6'' specifies a hexagon. This list, which comes from a ''recipe'' for making ) that consists of the positions of the 12 pentagons (1,2,3,4,8,9,10,12,13,14,15,18,20). Lists for 36-15 could start on any of the 20 faces and go backward as well as forward, in this case without any replicates, a total of 40 lists. ...
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 <or= 60, excluding those with any of the six configurations leaves just 15 cages plus buckminsterfullerene (n = 60), among them the known clathrin cages. Of the 216,739 mathematically possible cages for 60 < n <or= 84, just the 50 that obey the isolated-pentagon rule, among them known carbon cages, pass. The absence of likely fullerenes for some n (30,34,46,48,52-58,62-68) explains the abundance of certain cages, including buckminsterfullerene. These principles also suggest a "probable roads" path to self-assembly in place of pentagon-road and fullerene-road hypotheses.
