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High-grade gliomas with arginine or valine substitutions of the histone H3.3 glycine-34 residue (H3.3G34R/V) carry a dismal prognosis, and current treatments, including radiotherapy and chemotherapy, are not curative. Because H3.3G34R/V mutations reprogram epigenetic modifications, we undertook a comprehensive epigenetic approach using ChIP sequencing and ChromHMM computational analysis to define therapeutic dependencies in H3.3G34R/V gliomas. Our analyses revealed a convergence of epigenetic alterations, including (i) activating epigenetic modifications on histone H3 lysine (K) residues such as H3K36 trimethylation (H3K36me3), H3K27 acetylation (H3K27ac), and H3K4 trimethylation (H3K4me3); (ii) DNA promoter hypomethylation; and (iii) redistribution of repressive histone H3K27 trimethylation (H3K27me3) to intergenic regions at the leukemia inhibitory factor (LIF) locus to drive increased LIF abundance and secretion by H3.3G34R/V cells. LIF activated signal transducer and activator of transcription 3 (STAT3) signaling in an autocrine/paracrine manner to promote survival of H3.3G34R/V glioma cells. Moreover, immunohistochemistry and single-cell RNA sequencing from H3.3G34R/V patient tumors revealed high STAT3 protein and RNA expression, respectively, in tumor cells with both inter- and intratumor heterogeneity. We targeted STAT3 using a blood-brain barrier–penetrable small-molecule inhibitor, WP1066, currently in clinical trials for adult gliomas. WP1066 treatment resulted in H3.3G34R/V tumor cell toxicity in vitro and tumor suppression in preclinical mouse models established with KNS42 cells, SJ-HGGx42-c cells, or in utero electroporation techniques. Our studies identify the LIF/STAT3 pathway as a key epigenetically driven and druggable vulnerability in H3.3G34R/V gliomas. This finding could inform development of targeted, combination therapies for these lethal brain tumors.

“The means by which enlightened rulers and sagacious generals moved and conquered others, that their achievements surpassed the masses, was advance knowledge. Advance knowledge cannot be gained from ghosts and spirits, inferred from phenomena, or projected from the measures of heaven, but must be gained from men, for it is the knowledge of the enemy’s true situation.” Sun Tze, Bing Fa, 13 (perhaps 500 BC). “Nam et ipsa scientia potestas est.” [For knowledge itself is power] Francis Bacon (1561–1626) (Religious Meditations—Of Heresies). “I am selling what the whole world wants: power.” Matthew Boulton (1711–1780) (Letter to Catherine the Great of Russia, offering steam engines for sale). “Modern industry has established the World Market.” Karl Marx and Friedrich Engels, (The Communist Manifesto, 1848). “The fundamental concept in social science is Power, in the same sense in which Energy is the fundamental concept in physics.” Bertrand Russell (1872–1970) (“Power: A New Social Analysis,” 1938)

Now, 25 years or so after the quasi-crystal affair, we can perhaps see the development of crystallography, as it turns into nanotechnology and molecular biology, in a still longer-term perspective as part of the struggle to understand the universe rationally in the face of competing theories and superstitions. We follow changes of paradigm in investigations of the structure of matter and in various dualities, in particular in the dialogue between materials and information. In a small way, the discovery of quasi-crystals exhibits the interactions between the different world representations, Platonic, mental and physical (here labelled P, Q, R) and between conceptions of Laws, Natural, Mathematical, Civil/Military and Divine.

High-grade gliomas harboring H3 G34R/V mutations exclusively occur in the cerebral hemispheres of adolescents and young adults, suggesting a distinct neurodevelopmental origin. Combining multimodal bulk and single-cell genomics with unbiased genome-scale CRISPR/Cas9 approaches, we here describe a GABAergic interneuron progenitor lineage as the most likely context from which these H3 G34R/V mutations drive gliomagenesis, conferring unique and tumor-selective gene targets essential for glioma cell survival, as validated genetically and pharmacologically. Phenotypically, we demonstrate that while H3 G34R/V glioma cells harbor the neurotransmitter GABA, they are developmentally stalled, and do not induce the neuronal hyperexcitability described in other glioma subtypes. These findings offer a striking counter-example to the prevailing view of glioma origins in glial precursor cells, resulting in distinct cellular, microenvironmental, and therapeutic consequences.

The HERBY trial was a phase-II open-label, randomised, multicentre trial evaluating bevacizumab in addition to temozolomide/radiotherapy in patients with newly-diagnosed non-brainstem high-grade glioma between the ages of 3-18 years. We collected specimens from 89/113 patients consenting to translational research, and carried out comprehensive molecular analysis integrated with pathology, radiology and immune profiling. 7/89 patients harboured H3F3A_G34R/V mutations (diffusely infiltrative with predominant deep left temporoparietal involvement), whilst 24/89 harboured H3F3A_K27M, both conferring a worse outcome. Of the latter, two patients had distinct, separate lesions in the thalamus and hypothalamus, whilst the remaining had symmetrical central thalamic and midbrain localization. Four older patients had tumours harbouring IDH1 mutations, whilst three younger patients had tumours which by methylation profiling resembled low grade lesions; both of these hemispheric subgroups had a significantly longer survival. Hypermutator tumours (driven by mismatch repair deficiency and somatic POLE / POLD1 mutations) and those biologically resembling pleomorphic xanthoastrocytoma (PXA-like, driven by BRAF_V600E or NF1 mutation) had an elevated immune response in the form of CD8-positive tumour infiltrating lymphocytes (p=0.0018), and had longer overall survival in the bevacizumab arm (p=0.0489). Histone H3 subgroups (hemispheric G34R/V and midline K27M) had a worse outcome and were immune cold. Although the experimental arm did not improve survival across the whole cohort, we identify disease subgroups with MAPK activation to harbour an enhanced immune response and derive benefit from the addition of bevacizumab to standard temozolomide/radiotherapy.

Chemical gardens in laboratory chemistries ranging from silicates to polyoxometalates, in applications ranging from corrosion products to the hydration of Portland cement, and in natural settings ranging from hydrothermal vents in the ocean depths to brinicles beneath sea ice. In many chemical-garden experiments, the structure forms as a solid seed of a soluble ionic compound dissolves in a solution containing another reactive ion. In general any alkali silicate solution can be used due to their high solubility at high pH. The cation should not precipitate with the counterion of the metal salt used as seed. A main property of seed chemical-garden experiments is that initially, when the fluid is not moving under buoyancy or osmosis, the delivery of the inner reactant is diffusion controlled. Another experimental technique that isolates one aspect of chemical-garden formation is to produce precipitation membranes between different aqueous solutions by introducing the two solutions on either side of an inert carrier matrix. Chemical gardens may be grown upon injection of solutions into a so-called Hele-Shaw cell, a quasi-two-dimensional reactor consisting in two parallel plates separated by a small gap.

The lateral ventricle subventricular zone (SVZ) is a frequent and consequential site of pediatric and adult glioma spread, but the cellular and molecular mechanisms mediating this are poorly understood. We demonstrate that neural precursor cell (NPC):glioma cell communication underpins this propensity of glioma to colonize the SVZ through secretion of chemoattractant signals toward which glioma cells home. Biochemical, proteomic, and functional analyses of SVZ NPC-secreted factors revealed the neurite outgrowth-promoting factor pleiotrophin, along with required binding partners SPARC/SPARCL1 and HSP90B, as key mediators of this chemoattractant effect. Pleiotrophin expression is strongly enriched in the SVZ, and pleiotrophin knockdown starkly reduced glioma invasion of the SVZ in the murine brain. Pleiotrophin, in complex with the binding partners, activated glioma Rho/ROCK signaling, and ROCK inhibition decreased invasion toward SVZ NPC-secreted factors. These findings demonstrate a pathogenic role for NPC:glioma interactions and potential therapeutic targets to limit glioma invasion.

Cell migration through the brain parenchyma underpins neurogenesis and glioblastoma (GBM) development. Since GBM cells and neuroblasts use the same migratory routes, mechanisms underlying migration during neurogenesis and brain cancer pathogenesis may be similar. Here, we identify a common pathway controlling cell migration in normal and neoplastic cells in the CNS. The nuclear scaffold protein promyelocytic leukemia (PML), a regulator of forebrain development, promotes neural progenitor/stem cell (NPC) and neuroblast migration in the adult mouse brain. The PML pro-migratory role is active also in transformed mouse NPCs and in human primary GBM cells. In both normal and neoplastic settings, PML controls cell migration via Polycomb repressive complex 2 (PRC2)-mediated repression of Slits, key regulators of axon guidance. Finally, a PML/SLIT1 axis regulates sensitivity to the PML-targeting drug arsenic trioxide in primary GBM cells. Taken together, these findings uncover a drug-targetable molecular axis controlling cell migration in both normal and neoplastic cells.

Paediatric high grade glioma and diffuse midline glioma (including DIPG) are comprised of multiple biological and clinical subgroups, the majority of which urgently require novel therapies. Patient-derived in vitro primary cell cultures represent potentially useful tools for mechanistic and preclinical investigation based upon their retention of key features of tumour subgroups under experimental conditions amenable to high-throughput approaches. We established 21 novel primary cultures derived from patients in London, Dublin and Rome, and together with cultures shared from Barcelona, Brisbane and Stanford we assembled a panel of 42 models under 2D (laminin matrix) and/or 3D (neurospheres) conditions, fully credentialed by phenotypic and molecular comparison to the original tumour sample (methylation BeadArray, panel/exome sequencing, RNAseq). Screening against a panel of ~400 approved chemotherapeutics and small molecules, we identified specific dependencies associated with tumour subgroups and/or specific molecular markers. Examples included cells with sensitizing (HSJD-GBM-001, PDGFRA_A385ins; HSJD-DIPG-008, PDGFRA_D846N) or resistance (HSJD-GBM-002, PDGFRA_D842Y) mutations to a range of PDGFRA inhibitors, and individual models showing profound sensitivity to multiple FGFR (QCTB-R006) or EGFR (HSJD-DIPG-012) inhibitors. H3.3G34R cells were differentially sensitive to agents targeting the proteasome, whilst H3.3 K27M cells were responsive to crizotinib. MAPK-dysregulated PXA-like cultures differentially responded to inhibitors of upstream signalling via PKC and CK2. In total, 85% cells were found to have at least one drug screening hit in short term assays linked to the underlying biology of the patient’s tumour, providing a rational approach for individualised clinical translation.

Categories of the generalized crystallography, where structures are tiled into a large number of identical cells, include quasi-identity and quasi-equivalence. The hierarchy of organization levels including the n-dimensional space is considered. In the theory of proportions, irrational numbers, such as e, π, τ, etc., play an important role. The golden ratio τ is basic to the geometry of structures with five- or tenfold symmetry that are called quasi-crystals. The irrational nature of these numbers probably means that in the Euclidean space E3, we deal with projections of the fundamental polyhedra from a higher-dimensional space. Thus, the structures of quasi-crystals in the three-dimensional space represent slices of much more complex assemblies in the higher-dimensional space.

INTRODUCTION: The HERBY trial assessed the efficacy of adding Bevacizumab (BEV) to postoperative radiotherapy/temozolamide (RT/TMZ) in children with newly diagnosed non-pontine high-grade gliomas (HGG). The trial showed no difference in OS or EFS between BEV and non-BEV treatment arms. METHODS: Radiological, pathological and molecular data were evaluated to characterise pediatric HGG and correlate with outcome measures. RESULTS: 74/124 (59.7%) patients had Cerebral hemispheric and 50/124 (40.3%) Midline tumors. Pathological diagnosis was available in all cases (111 astrocytomas /124), molecular data in 89/124. K27M histone mutations were present in 24/33 Midline cases with molecular data, and G34R/V mutations in 7 Cerebral cases. 116 patients completed treatment (RT/TMZ=56, BEV=60). 54/70 (77%) Cerebral cases underwent total/near-total resection with debulking/biopsy in 16/70 (23%). Fewer (12/46) Midline tumors had total/near-total resections than debulking/biopsy (34/46) (p

The structural chemistry of the lovozerite group of minerals is considered using concepts of coordination polyhedra, finite automata and local order. A formal language for these lovozerite-type structures is constructed and the concept of a genetic code for this structure family is suggested. Information and structure are seen to be dialectically interlinked.

The principles of algebraic geometry have been applied for the modelling of substances of different natures. A local packing approach provides a tool for constructing not only the special icosa-geodesic 2D tilings of a sphere but also the 3D tilings of spherical layers. The structures of the pseudo-T = 7 polyoma and papilloma viral capsids can thus be modelled. This general approach is applicable to inorganic, organometallic, and biological nanoparticles.

In icosahedral carbon nanoparticles, the diamond-like core can undergo a reversible topological transition into and coexist coherently with the onion shells., The general approach for describing and designing complex hierarchical icosahedral structures is discussed. Structural models of icosahedral carbon nanoparticles in which the local arrangement of atoms is virtually identical to that in diamond are derived. It is shown that icosahedral diamond-like particles can be transformed into onion-like shell structures (and vice versa) by the consecutive smoothing (puckering) of atomic networks without disturbance of their topological integrity. The possibility of coherent coexistence of icosahedral diamond-like core with onion shells is shown.

Desmond Bernal was one of the most remarkable figures of his time, a visionary, a founder of molecular biology, one of the great intellectuals of the twentieth century. This paper looks at the man himself, his work and his influence and reconstructs some of the vast network connecting Bernal with the people and events of his times.

Pseudoprogression (PsP) is a treatment-related phenomenon which hinders response interpretation. Its prevalence and clinical impact have not been evaluated in children/adolescents. We assessed the characteristics, risk factors and prognosis of PsP in children/adolescents and young-adults diagnosed with non-brainstem high grade gliomas (HGG) and diffuse intrinsic pontine gliomas (DIPG). Patients aged 1-21 years diagnosed with HGG or DIPG between 1995 and 2012 who had completed radiotherapy were eligible. PsP was assessed according to study-specific criteria and correlated with first-line treatment, molecular biomarkers and survival. Ninety-one patients (47 HGG, 44 DIPG) were evaluable. Median age: 10 years (range, 2-20). Eleven episodes of PsP were observed in 10 patients (4 HGG, 6 DIPG). Rates of PsP: 8.5 % (HGG); 13.6 % (DIPG). Two episodes of PsP were based on clinical findings alone; nine episodes had concurrent radiological changes: increased size of lesions (n = 5), new focal enhancement (n = 4). Temozolomide, MGMT methylation or H3F3A mutations were not found to be associated with increased occurrence of PsP. For HGG, 1-year progression-free survival (PFS) was 41.9 % no-PsP versus 100 % PsP (p = 0.041); differences in 1-year overall survival (OS) were not significant. For DIPG, differences in 1-year PFS and OS were not statistically significant. Hazard ratio (95 %CI) of PsP for OS was 0.551 (0.168-1.803; p = 0.325) in HGG; and 0.308 (0.107-0.882; p = 0.028) in DIPG. PsP occurred in both pediatric HGG and DIPG patients at a comparable rate to adult HGG. PsP was associated with improved 1-yr PFS in HGG patients. PsP had a protective effect upon OS in DIPG patients.

A major challenge to improve outcomes in paediatric GBM and DIPG is their extensive intratumoral heterogeneity, reflected by differing cellular morphologies and genomic imbalances present within an individual sample. This is apparent also at the mutational level, where a complex subclonal architecture can be inferred from bulk tumour sequencing at diagnosis/biopsy and at relapse/autopsy. Spatial heterogeneity is also observed by studying multiple topographically distinct regions from the same tumour. We sought to understand the relative functional contributions of these subclonal cell populations to tumour development and evolution. We have established 20 primary patient-derived cultures (10 pGBM, 10 DIPG), with extensive phenotypic and genomic characterisation to ensure accurate recapitulation of the original disease. Single cells were flow-sorted into individual wells in a 96-well format and allowed to form colonies under stem cell conditions on laminin-coated plates (2D) or as neurospheres (3D). Individual colonies were subjected to high-throughput image analysis and targeted re-sequencing. Clonogenicity ranged from 0-20%, significantly higher in H3.3K27M mutant cells. Such an approach allowed for the isolation of single stem cell-derived colonies harbouring clonal mutations, some of which were present in only a small proportion of the original sample, such as a truncating mutation in the histone H4K20 methyltransferase SUV420H1 in a DIPG sample, originally found in 2/678 reads by targeted resequencing. Comparing colonies harbouring this mutation with their ‘natural isogenic’ counterparts with an otherwise identical genetic background, we observed significantly increased invasion and migration in the SUV420H1 mutant cells. Notably, bulk cultures containing mixtures of these distinct subpopulations were found to have additionally enhanced pro-tumorigenic potential than either colony alone. These data identify a distinct genetic and functional diversity in paediatric glioma stem cell populations, and suggest a co-operativity of tumour subclones. Treatment strategies aimed at disrupting these interactions may represent a novel therapeutic approach in these diseases.

Recent molecular profiling studies of paediatric high grade (pHGG) and diffuse intrinsic pontine glioma (DIPG) have refined these tumours into age- and location-based subgroups driven by unique genetic and epigenetic alterations, however individual studies are underpowered to investigate subgroup-specific events. We have retrieved publicly available genome-wide data from ∼560 pHGG/DIPG samples and combined this with ∼140 unpublished cases including young adults up to the age of 30 years. We have integrated multiple array-based and sequencing platforms to produce DNA copy number profiles from ∼700 tumours, ∼500 with clinicopathological and histone H3 annotation, and >300 of which have full somatic sequence information. We identified subgroup-specific genetic alterations co-segregating, or mutually exclusive, with known driving histone mutations. H3.3G34R/V cerebral hemispheric tumours harbour significantly more CNAs and SNVs than other subgroups. These included novel amplified loci at 1p13.3 (KCNA) and a histone cluster at 6p22.2, though lacked key amplified loci such as MYC/MYCN. H3.1K27M DIPG were distinct from H3.3K27M primarily on the basis of whole arm chromosomal changes (enriched +2, -16q; reduced -17p and a lack of TP53 mutations). H3.3K27M tumours harboured specifically enriched known (7q31.2;MET) and novel amplicons (17p11.2;TOP3A). Integration with mutation data identified subgroup-independent, non-overlapping pathway-level recurrent alterations, such as RTK-PI3K-mTOR, dysregulated in 55% cases and conferring shorter survival in hemispheric, but not other locations. As well as inter-tumoral differences, deeper interrogation of the sequencing data also reveals substantial intra-tumoral heterogeneity. Whilst driving histone H3 mutations were found to be present in 100% of cells, mutations in genes such as PDGFRA and PIK3CA were predominantly found at subclonal levels, and tumours from all locations were inferred to be comprised of multiple subclonal populations, with H3.3G34R/V the most genetically diverse. These data improve our understanding of the underlying biology of pHGG/DIPG, and will provide rational targets for subgroup-specific and –independent therapies.

Approximately 1% of all paediatric brain tumours occur at less than one year of age, and glioblastoma (GBM) account for only 2-9% of these. Their clinical presentation, location, histology, behaviour, response to therapy and outcome differ from GBMs of older children and adults, and they do not appear to be associated with known histone H3 or IDH1-driven subgroups. Recent genome and RNA sequencing data highlighted recurrent NTRK1-3 fusions in 4/10 non-brainstem GBM under the age of 3 years, including one case of ETV6-NTRK3 in a cerebral hemispheric tumour diagnosed at 1 month old. These fusions are usually associated with congenital mesoblastic nephroma and congenital infantile fibrosarcoma, and upon review of a series of cases diagnosed as glioblastoma under the age of 1yr, 6/14 were found to present with a predominant spindle cell morphology, a relatively circumscribed interface with adjacent brain, and without prominent infiltration. These tumours were positive for GFAP as well as desmin, CD56 and CD99. One case was diagnosed in utero by ultrasound, and at birth underwent surgical resection from which primary cell cultures were established under stem cell conditions on laminin-coated plates. Exome and RNA sequencing revealed the presence of the ETV6:NTRK3 fusion transcript as the sole somatic alteration, validated by RT-PCR, Sanger sequencing and FISH. 450K methylation profiling clustered the tumour with desmoplastic infantile ganglioglioma rather than subgroups of paediatric GBM. Primary cells treated with the CNS-penetrant small molecule Trk inhibitor PHA-848125, resulted in marked sensitivity (GI50 = 200nM) compared to cerebral hemispheric (H3 wild-type) and thalamic (H3.3K27M) paediatric GBM cells (GI50 = 1.8-4.6mM). A subset of infantile/congenital brain tumours classified as GBM appear to represent a distinct entity more closely related, biologically and histologically, to mesenchymal cancers. Agents targeting ETV:NTRK3 may be a useful novel treatment strategy in these children.

In nature there are numerous layered compounds, some of which could be curved so as to form fascinating nanoshapes with novel properties. Graphite is at present the main example of a very flexible layered structure, which is able to form cylinders (nanotubes) and cages (fullerenes), but there are others. While fullerenes possess positive curvature due to pentagonal rings of carbon, there are other structures which could include heptagonal or higher membered rings. In fact, fullerenes and nanotubes could display negative curvature, thus forming nanomaterials possessing unexpected electronic and mechanical properties. The effect of curvature in other nano-architectures, such as in boron nitride and metal dichalcogenides, is also discussed in this account. Electron irradiation is a tool able to increase the structural complexity of layered materials. In this context, we describe the coalescence of carbon nanotubes and C(60) molecules. The latter results now open up an alternative approach to producing and manipulating novel nanomaterials in the twenty-first century.

Extrapolating from human history, science is seen as having ever enhancing responsibility in surviving the future.

We must conclude that the sub-title of Bernal’s “The Social Function of Science” — “What science does: what science could do” is still the relevant challenge and indicates Bernal’s chief contribution, besides the foundation of molecular biology to our civilization. It is manifest that resources spent on armaments are a monstrous pathological symptom of our social structure. The ancient problem of “what is property” and what may be “owned” and by whom or by what organs of society is awakening.

Paediatric high grade glioma (pHGG) and DIPG are defined by recurrent mutations in H3 histones, as well as frequent alterations in the chromatin remodeling protein ATRX. This is strongly associated with the alternative lengthening of telomeres (ALT) phenotype, but their precise interaction with histone mutations and their role in tumorigenesis remain unclear. We collected sequence data from 262 published and 64 unpublished cases of pHGG/DIPG and identified somatic ATRX mutations in 54/326(17%) of cases. The majority of frameshift mutations (37/54,68.5%) were found in the ADD domain, whereas missense mutations (16/54,29.6%) were almost exclusively in the helicase domain (11/54, 20,4%). ATRX mutations commonly co-segregate with H3.3G34 (16/54,29.6%) and TP53 (42/54,77.8%) mutations, and define a subgroup of patients with a longer overall survival (p=0.079), though with a greater number of somatic mutations (p=0.023) and copy number alterations (p=0.0011) than wild-type cases. We subjected a series of fully characterised primary patient-derived pHGG/DIPG cell cultures to high-throughput in vitro cell viability screening of >400 chemotherapeutics and small molecules. We identified a genetic dependency for ATRX mutation and sensitivity to distinct PARP inhibitor chemotypes, including olaparib and rucaparib (catalytic inhibitors), and talazoparib (PARP trapper), validated using CRISPR/Cas9-engineered ATRX knockout targeting either the ADD or helicase domain in pHGG cells. ATRX-deficient cells were also more sensitized to radiation treatment by PARP inhibition compared to wild-type controls. Gene expression analysis of ATRX mutant pHGG/DIPG samples confirmed an intact homologous recombination pathway and overexpression of PARP1, suggesting an underlying mechanism distinct from that observed in BRCA-mutant breast and ovarian cancers. Ongoing work is aimed at unravelling the specific pathways involved, and evaluating the utility of PARP inhibition in orthotopic pGBM xenografts in vivo. These data suggest a synthetic lethality for PARP inhibitors in ATRX-deficient pHGG/DIPG cells, and may represent a novel therapeutic strategy for these highly aggressive tumours.

By the materials of the lecture delivered in the School on Electron Crystallography, Erice, Sicily, 1997 and published in Proceedings of NATO Advanced Study Institute on Electron Crystallography, Erice, Sicily, 1997, Series E, vol. 347, p. 1.

The cubic P , G , D and I-WP triply periodic minimal surfaces (TPMS) may be closely approximated using periodic nodal surfaces (PNS) with few Fourier terms, thus enabling easy generation of TPMS for use in various chemical and physical applications. The accuracy of such approximations is quantitatively discussed and represented visually using a colour coding.

Parametric expressions for the coordinates of Schwarz's D triply periodic minimal surface, found in many diverse physical, chemical and biological systems, allow us to describe fully the properties of the surface and to demonstrate its straightforward exact computation. Knowledge of the precise coordinates of the surface enables real structures to be quantified in terms of the parameters of the surface. q 1999 Elsevier Science B.V. All rights reserved.

The systematic enumeration of all possible networks of atoms in inorganic structures is of considerable interest. Of particular importance are the 4-connected networks (those in which each. atom is connected to exactly four neighbours), which are relevant to a wide range of systems-crystalline elements, hydrates, covalently bonded crystals, silicates and many synthetic compounds. Systematic enumeration is especially desirable in the study of zeolites and related materials, of which there are now 121 recognized structural types(1), with several new types being identified every year. But as the number of possible 4-connected three-dimensional networks is infinite, and as there exists no systematic procedure for their derivation, the prediction of new structural types has hitherto relied on empirical methods (see, for example, refs 2-4). Here we report a partial solution to this problem, based on recent advances in mathematical tiling theory(5-8). We establish that there are exactly 9, 117 and 926 topological types of, respectively, 4-connected uninodal, binodal and trinodal networks, derived from simple tilings based on tetrahedra. (Here nodality refers to the number of topologically distinct vertices from which the network is composed.) We also show that there are at least 145 more distinct uninodal networks based on a more complex tiling unit. Of the total number of networks that we have derived, only two contain neither three- nor four-membered ring, and most of the binodal and trinodal networks are new.

The concept of projection from one space to another, with a consequent loss of information, can be seen in the relationships of gene to protein and language description to real situation. Such a transformation can only be reversed if extra external information is re-supplied. The genetic algorithm embodying this idea is now used in applied mathematics for exploring a configuration space. Such a dialectic – transformation back and forth between two kinds of description – extends the traditional Hegelian concept used by Engels and others of change as resulting from a resolution of the conflict of two opposing tendencies and provides for evolution of the joint system.

The bulk of the 'silica garden', made by seeding a solution of sodium silicate with crystals of aluminium nitrate, is an amorphous aluminosilicate. Transmission electron microscopy reveals a hierarchic substructure involving fine tubes f 44 . nm in diameter composed of amorphous silica rods. It is also possible that the macroscopic fibres seen by scanning electron microscopy contain periodic arrays of microtubules f 4.4 mm in diameter. q 1998 Elsevier Science B.V.

Two samples of hydrated silica from the bamboo plant (‘tabasheer’ and ‘bambusa’) were examined by X-ray fluorescence and 1H, 27Al and 29Si solidstate NMR, X-ray diffraction and thermogravimetric analysis. Silicon is the major elemental component of both samples, with much smaller amounts of aluminium (about 1·2 wt%), iron (0·3—0·4 wt%), calcium and magnesium, and traces of phosphorus. The maximum theoretical water loss calculated from the OH/Si ratio derived from the 29Si NMR spectra (4·92 and 3·82 wt% for the two samples) agrees with the weight loss measured by thermogravimetric analysis. Adsorbed water is evolved at temperatures below about 250°C, which is followed by gradual dehydroxylation. The water content of tabasheer is greater than that of bambusa, so that the initial rate of weight loss in both in tabasheer is higher. However, above about 250°C the rate of weight loss in both samples is very similar and the thermogravimetric curves are virtually parallel. The weight loss on dehydroxylat...

A world view deriving from the objective knowledge acquired by the physical sciences is contrasted with the fashionable subjective philosophical view that all systems of thought are equally valid ways of structuring the universe. As Lucretius guessed, atoms are real and are not simply arbitrary constructs to explain the observations. Mathematics and computing have an important role in permitting long and sophisticated arguments to be carried through.

With the discovery of C60 or Buckminsterfullerene a new kind of materials with important applications has emerged. Orginary graphite is composed of flat hexagonal layers. If pentagons are introduced, the graphite sheets start to curve in such a way that 12 pentagons are needed to close the structure and form fullerenes. Starting from the properties of 2D manifolds or surfaces, we have found that by introducing rings with more than six carbon atoms, periodic structures with the same topology as triply periodic minimal surfaces, we have found that by introducing rings with more than six carbon atoms, periodic structures with the same topology as triply periodic minimal surfacds can be constructed. The D, G, P, H and I-WP type surfaces have been obtained from graphite-like sheets. In terms of the Gaussian curvature K, ordinary and cylindrical graphite have K=O, Fullerenes have K>O and triply periodic surfaces decorated with graphite have K

The geometry of rings with 5, 6, 7, 8 and 9 links, particularly those with seven links such as occur in cyclo‐heptane and analogous molecules* is re‐considered with the aid of distance geometry, now more practicable with modern mathematical software. Use is made of a quadric surface which may be fitted to nine points.

With the formalism of differential geometry, implemented in modern computer graphics, mathematical structures have been developed which provide the underlying geometry for an increasing range of real structures more general than crystals and occurring both in biology and in materials science. In particular the triply periodic minimal surfaces (TPMS) are examined.

Categories of the generalized crystallography, where structures are tiled by a large number of identical cells, include quasi-identity and quasi-equivalence. The hierarchy of the organization levels is considered, involving the n-D space. In the theory of proportions, the irrational numbers, such as e, ί, π, and τ, play an important role. The golden-ratio number τ is fundamental for the geometry of structures with five- or tenfold symmetry, eventually called quasicrystals. The fact that these numbers are irrational suggests that in the Euclidean space E3, we observe the projections of the fundamental polyhedra from a higher-dimensional space. Thus, complex crystal (or quasicrystal) structures are only cells of some much more complex assemblies of higher dimensionality.

We argue for a convergence of crystallography, materials science and biology, that will come about through asking materials questions about biology and biological questions about materials, illuminated by considerations of information. The complex structures now being studied in biology and produced in nanotechnology have outstripped the framework of classical crystallography, and a variety of organizing concepts are now taking shape into a more modern and dynamic science of structure, form and function. Absolute stability and equilibrium are replaced by metastable structures existing in a flux of energy-carrying information and moving within an energy landscape of complex topology. Structures give place to processes and processes to systems. The fundamental level is that of atoms. As smaller and smaller groups of atoms are used for their physical properties, quantum effects become important; already we see quantum computation taking shape. Concepts move towards those in life with the emergence of specifically informational structures. We now see the possibility of the artificial construction of a synthetic living system, different from biological life, but having many or all of the same properties. Interactions are essentially nonlinear and collective. Structures begin to have an evolutionary history with episodes of symbiosis. Underlying all the structures are constraints of time and space. Through hierarchization, a more general principle than the periodicity of crystals, structures may be found within structures on different scales. We must integrate unifying concepts from dynamical systems and information theory to form a coherent language and science of shape and structure beyond crystals. To this end, we discuss the idea of categorizing structures based on information according to the algorithmic complexity of their assembly.

We have extended the use of the invariants of spherical harmonics for the characterisation of the angular distribution of coordinating atoms about a central atom. These invariants are suitable indices for use in clustering algorithms for automatic crystal chemistry. Invariants for coordination polyhedra in intermetallic compounds and Ca-O silicates are considered. A study of invariants in coordination polyhedra distorted by the Jahn-Teller effect is presented. In addition, Invariants from small clusters and the cuboctahedron-icosahedron transition are analyzed.

The Weierstrass representation has been used to construct negatively curved graphite in which atoms rest no a perfect triply periodic minimal surface. By applying the Bonnet transformation on a patch of the D surface decorated with graphite we have been able to construct the Gyroid and P minimal surfaces. Curvatures, densities and lattice parameters have been calculated. It has been found that the maximum Gaussian curvature for our negatively curved structures is less in magnitude than the Gaussian curvature ofC 60. In addition, a new periodic graphitic set with the same topology as the I-WP minimal surface has been obtained by introducing pentagonal and octagonal rings.

A method has been developed for binding numerically the minimal (soap-film) surface bounded a skew quadrilateral. A general quartic is fitted to each patch in turn and the local curvature is adjusted appriately. Using this, the P and D periodic minimal surfaces have each been expressed as the nodal surface of an expression which is the sum of Fourier terms each corresponding to a set of planes {ith, k, l} in the appropriate space group. Thus, the exact minimal surface (or any other surface such as an equipotential) can be expressed to any required accuracy as a sum of trigonometric functions which are readily calculable. The method is capable of generalisation.