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PubMed2001

Percolation clustering: a novel approach to the clustering of gene expression patterns in Dictyostelium development.

We present a novel approach to the clustering of gene expression patterns based on the mutual connectivity of the patterns. Unlike certain widely used methods (e.g., self-organizing maps and K-means) which essentially force gene expression data into a fixed number of predetermined clustering structures, our approach aims to reveal the natural tendency of the data to cluster, in analogy to the physical phenomenon of percolation. The approach is probabilistic in nature, and as such accommodates the possibility that one gene participates in multiple clusters. The result is cast in terms of the connectivity of each gene to a certain number of (significant) clusters. A computationally efficient algorithm is developed to implement our approach. Performance of the method is illustrated by clustering both constructed data and gene expression data obtained from Dictyostelium development.

Algorithms↗
PubMedDate not supplied

Clustering of cases of type 1 diabetes mellitus occurring 2-4 years after vaccination is consistent with clustering after infections and progression to type 1 diabetes mellitus in autoantibody positive individuals.

OBJECTIVE: We previously analyzed data from a hemophilus vaccine trial and identified clusters of extra cases of type 1 diabetes mellitus (T1DM) caused by the vaccine that occurred between 36 and 48 months after immunization. Published reports indicate clustering of cases of T1DM occurring approximately 2-4 years after mumps infection. Others have reported a 2-4 year delay between the onset of autoantibodies and the development of T1DM. We attempted to determine whether similar clustering of cases of T1DM occurred after immunization with vaccines other than hemophilus. METHODS: We searched MEDLINE and reviewed references from published papers to find databases on the incidence of T1DM and then searched MEDLINE to determine whether changes in immunization occurred in these regions during the times the incidence of DM was being recorded. RESULTS: Distinct rises in the incidence of T1DM occurred 2-4 years following the introduction of the MMR and pertussis vaccines. A drop in the incidence of T1DM was detected between 3-4 years following discontinuation of pertussis and BCG vaccines. CONCLUSION: The identification of clusters of cases of T1DM occurring in consistent temporal time periods allowed a link between the hemophilus vaccine and T1DM to be established. The current findings indicate the there are also clusters of cases of T1DM occurring 2-4 years post-immunization with the pertussis, MMR, and BCG vaccine. The data are consistent with the occurrence of clusters following mumps infection and the progression to T1DM in patients with antipancreatic autoantibodies.

Autoantibodies↗
PubMed1998

Between- and within-cluster covariate effects in the analysis of clustered data.

Standard methods for the regression analysis of clustered data postulate models relating covariates to the response without regard to between- and within-cluster covariate effects. Implicit in these analyses is the assumption that these effects are identical. Example data show that this is frequently not the case and that analyses that ignore differential between- and within-cluster covariate effects can be misleading. Consideration of between- and within-cluster effects also helps to explain observed and theoretical differences between mixture model analyses and those based on conditional likelihood methods. In particular, we show that conditional likelihood methods estimate purely within-cluster covariate effects, whereas mixture model approaches estimate a weighted average of between- and within-cluster covariate effects.

Adolescent↗
PubMed1986

HLA-DR2-associated Dw subtypes correlate with RFLP clusters: most DR2 IDDM patients belong to one of these clusters.

Two variants of the serologically defined HLA-DR2 specificity have been reported: DR2 long and DR2 short. Distinct HLA-DR2-associated Dw subtypes have been described at the cellular level. In the Israeli population, DR2 individuals may be grouped into three clusters: DR2/Dw2, DR2/Dw12, and DR2/Dw"AZH". A new approach for the study of the polymorphism of HLA class II genes is to investigate restriction endonuclease fragments obtained from genomic DNA with specific class II cDNA probes. Previous analysis of DQ beta restriction endonuclease fragments subdivided the DR2 haplotypes into two subsets: a DQR1-positive subset and a DQR2.6-positive subset. These two subsets behave in the population as alleles that split HLA DQw1. In the present study, we have analyzed class II DQ alpha, DQ beta, and DR beta restriction fragment length polymorphism (RFLP) in HLA-DR2/Dw-typed healthy, unrelated Israeli individuals, as well as in 11 French HLA-DR2 insulin-dependent diabetes mellitus (IDDM) patients and 11 French DR-matched controls. Three DQ beta allelic clusters (DQR2.6, DQR1, and DQR12) were observed among the DR2 haplotypes and clearly correlated with Dw2, Dw"AZH", and Dw12, respectively. The vast majority of the DR2 IDDM patients (9 out of 11) fit into the DQR1 cluster which correlates with Dw"AZH", while only two patients (2 out of 11) belong to the DQR2.6 cluster (Dw2-like). In contrast, among 11 DR-matched healthy controls, 9 belonged to the DQR2.6 cluster and only 2 belonged to the DQR1 cluster. These studies establish the correlation between the DR2-associated Dw subtypes with specific RFLPs, and indicate that the frequency of the DQR1 subset which correlates with Dw"AZH" is increased in DR2 IDDM patients.

DNA Restriction Enzymes↗
PubMed2001

Effects of liquid phase composition on salt cluster formation in positive ion mode electrospray mass spectrometry: implications for clustering mechanism in electrospray.

Potassium bromate salt clusters, [KBrO3]nKx(x+), formed by electrospray ionization were studied as a function of solution properties. Clusters with up to 4 positive charges were observed. Their abundance, charge state and distribution were shown to vary with the organic solvent in solution. The effects of 7 solvents, including methanol, ethanol, isopropanol, acetonitrile, acetone, pyridine, and 1,4-dioxane, were thoroughly investigated. Solvents with a low dielectric constant and a high viscosity seem to favor clustering in solution but do not systematically allow high charge state ion formation. On the other hand, cluster charge reduction during desolvation was not correlated with solvent cation affinity over the range of solvents examined. However, ion distribution in mass spectra could be rationalized as a combination of these two competing phenomena. Charge state increases with the cluster size but may be reduced during ion desolvation when high cation affinity solvent molecules are actually involved in the ion solvation shell. This assumption could be envisaged in either Iribarne or Dole mechanisms of ion release in the gas phase. However, intensity profiles of multiply charged clusters could only be understood in terms of the ion evaporation mechanism.

Journal Article↗
PubMed2006

Effect of the cluster size on the micro phase separation in mixtures of beta-lactoglobulin clusters and kappa-carrageenan.

The phase separation of globular protein clusters formed by heat-denatured beta-lactoglobulin (beta-lg) in mixtures with the polysaccharide kappa-carrageenan (kappa-car) has been studied at pH 7 and 20 degrees C. The effect of the protein cluster size on the phase separation was investigated by preparing clusters with radii between 20 nm and 1 mum. The formation of protein rich microdomains led to an increase of the turbidity starting at a minimum kappa-car concentration that decreased with increasing cluster size, but was only weakly dependent on the protein concentration. The size and number of microdomains do not depend much on the cluster size, but their density decreases with increasing cluster size leading to a lower turbidity.

Carrageenan↗
PubMed2004

Application of a universal force field to mixed Fe/Mo-S/Se cubane and heterocubane clusters. 2. Substitution of iron by molybdenum in Fe4(S/Se)4 clusters with terminal halide and thiolate ligands.

Infrared and Raman spectra of Fe(4)(S/Se)(4) clusters with terminal halide ligands and MoFe(3)S(4) clusters with terminal thiolate and halide ligands are presented and interpreted on the basis of the force fields determined in the accompanying paper. The Raman spectra of halide coordinated Fe(4)(S/Se)(4) clusters are characterized by the fact that vibrations of the terminal ligands appear with little or vanishing intensity. Infrared and Raman spectra of MoFe(3)S(4) clusters with terminal thiolates are correlated to those of corresponding Fe(4)S(4) systems, which were investigated in part 1 of this study and interpreted with normal coordinate analysis. Band assignments are checked by employing MoFeS(4) clusters with terminal halide ligands. Spectra of these systems are in turn compared to those of their Fe(4)S(4) counterparts, i.e., Fe-S cubane clusters with chloro, bromo, and iodo ligands. A consistent interpretation of all spectra is presented. General implications of these results are discussed.

Journal Article↗
PubMed2006

Density functional theory study of 10-atom germanium clusters: effect of electron count on cluster geometry.

Density functional theory (DFT) at the hybrid B3LYP level has been applied to Ge10z germanium clusters (z = -6, -4, -2, 0, +2, +4, +6) starting from 12 different initial configurations. The D4d 4,4-bicapped square antiprism found experimentally in B10H102- and other 10-vertex clusters with 22 skeletal electrons is calculated for the isoelectronic Ge102- to be the global minimum by more than 15 kcal/mol. The global minima found for electron-rich clusters Ge104- and Ge106- are not those known experimentally. However, experimentally known structures for nido-B10H14 and the pentagonal antiprism of arachno-Pd@Bi104+ are found at higher but potentially accessible energies for Ge104- and Ge106-. The global minimum for Ge10 is the C3v 3,4,4,4-tetracapped trigonal prism predicted by the Wade-Mingos rules and found experimentally in isoelectronic Ni@Ga1010-. However, only slightly above this global minimum for Ge10 (+3.3 kcal/mol) is the likewise C3v isocloso 10-vertex deltahedron found in metallaboranes such as (eta6-arene)RuB9H9 derivatives. Structures found for more electron-poor clusters Ge102+ and Ge104+ include various capped octahedra and pentagonal bipyramids. This study predicts a number of 10-vertex cluster structures that have not yet been realized experimentally but would be interesting targets for future synthetic 10-vertex cluster chemistry using vertex units isolobal with the germanium vertices used in this work.

Journal Article↗
PubMed2006

Mo(W)/Cu/S cluster-based supramolecular arrays assembled from preformed clusters [Et4N]4[WS4Cu4I6] and [(n-Bu)4N]2[MoOS3Cu3X3] (X = I, SCN) with flexible ditopic ligands.

In our working toward the rational design and synthesis of cluster-based supramolecular architectures, a set of new [WS4Cu4]- or [MoOS3Cu3]-based supramolecular assemblies have been prepared from reactions of preformed cluster compounds [Et4N]4[WS4Cu4I6] (1) and [(n-Bu)4N]2[MoOS3Cu3X3] (2, X = I; 3, X = SCN) with flexible ditopic ligands such as dipyridylsulfide (dps), dipyridyl disulfide (dpds), and their combinations with dicyanamide (dca) anion and 4,4'-bipy. The cluster precursor 1 reacted with dps or dpds and sodium dicyanamide (dca) in MeCN to produce [WS4Cu4I2(dps)3].2MeCN (4.2MeCN) and [WS4Cu4(dca)2(dpds)2].Et2O.2MeCN (5.Et2O.2MeCN), respectively. On the other hand, treatment of 2 with dpds in DMF/MeCN afforded [MoOS3Cu3I(dpds)2].0.5DMF.2(MeCN)0.5 (6.0.5DMF.2(MeCN)0.5) while reaction of 3 with sodium dicyanamide (dca) and 4,4'-bipy in DMF/MeCN gave rise to [MoOS3Cu3(dca)(4,4'-bipy)1.5].DMF.MeCN (7.DMF.MeCN). Compounds 4.2MeCN, 5.Et2O.2MeCN, 6.0.5DMF.2(MeCN)0.5, and 7.DMF.MeCN have been characterized by elemental analysis, IR spectroscopy, and single-crystal X-ray crystallography. Compound 4 contains a 2D layer array made of the saddle-shaped [WS4Cu4] cores interlinked by three pairs of Cu-dps-Cu bridges. Compound 5 has another 2D layer structure in which the [WS4Cu4] cores are held together by four pairs of Cu-dca-Cu and Cu-dpds-Cu bridges. Compound 6 displays a 1D spiral chain structure built of the nido-like [MoOS3Cu3] cores via two pairs of Cu-dpds-Cu bridges. Compound 7 consists of a 2D staircase network in which each [MoOS3Cu3(4,4'-bipy]2 dimeric unit interconnects with four other equivalent units by a pair of 4,4'-bipy ligands and two pairs of dca anions. The [WS4Cu4] core in 4 or 5 and the [MoS3Cu3] core in 7 show a planar 4-connecting node and a seesaw-shaped 4-connecting node, respectively, which are unprecedented in cluster-based supramolecular compounds. The successful assembly of 4-7 from the three cluster precursors 1-3 through flexible ditopic ligands provides new routes to the rational design and construction of complicated cluster-based supramolecular arrays.

Journal Article↗
PubMed1998

Structure of LaMo(2)O(5) Containing Both Isolated Mo(6)O(18) Clusters and Sheets of Fused Triangular Mo(3) Clusters.

The structure of the disordered lanthanum molybdate, LaMo(2)O(5), has been solved and refined using powder neutron diffraction data collected at 300 K. The average structure is described in P6(3)/mmc, a = 8.373(1) Å, c = 19.1510(1) Å, Z = 12. The compound contains two types of Mo-Mo bonded units: isolated octahedral Mo(6)O(18) clusters, and infinite molybdenum oxide sheets, formed from condensed triangular Mo(3)O(13) clusters joined together to give a total of four Mo-Mo bonds for each molybdenum. The Mo(6)O(18) clusters have 16 electrons available for metal-metal bonding and the Mo-Mo distances within the unit are 2.643(4) Å x 6 and 2.695(5) Å x 6. In the infinite sheets the molybdenum-molybdenum distances are 2.612(9) Å within one equilateral triangular cluster and 2.621(8) Å within another. Each of the molybdenum atoms in the two different Mo(3) clusters has two molybdenum neighbors from the other cluster at a distance of 2.882(6) Å. Disorder in this layered structure occurs because of interchange of layers of Mo sheets with layers of lanthanum ions. The Bragg scattering is accounted for by including layers occupied with a 50% probability by each of these structural elements and their associated oxygen atoms. A model showing how ordered subunits are stacked together to produce the average structure is presented. Extended X-ray absorption fine structure spectroscopy (EXAFS) at the Mo K-edge was used to give information on the local structure around molybdenum and to confirm that the final structural model gives a good description of Mo-O and Mo-Mo bonding.

Journal Article↗
PubMed2003

Iron-sulfur cluster biosynthesis. Characterization of frataxin as an iron donor for assembly of [2Fe-2S] clusters in ISU-type proteins.

ISU (eukaryotes) and IscU (prokaryotes) are a homologous family of proteins that appear to provide a platform for assembly of [2Fe-2S] centers prior to delivery to an apo target protein. The intermediate [2Fe-2S] ISU-bound cluster is formed by delivery of iron and sulfur to the apo ISU, with the latter delivered through an IscS-mediated reaction. The identity of the iron donor has thus far not been established. In this paper we demonstrate human frataxin to bind from six to seven iron ions. Iron binding to frataxin has been quantitated by iron-dependent fluorescence measurements [K(D)(Fe(3+)) approximately 11.7 microM; (K(D)(Fe(2+)) approximately 55.0 microM] and isothermal titration calorimetry (ITC) [K(D)(Fe(3+)) approximately 10.2 microM]. Enthalpies and entropies for ferric ion binding were determined from calorimetric measurements. Both fluorescence (K(D) 0.45 microM) and ITC measurements (K(D) 0.15 microM) demonstrate holo frataxin to form a complex with ISU with sub-micromolar binding affinities. Significantly, apo frataxin does not bind to ISU, suggesting an important role for iron in cross-linking the two proteins and/or stabilizing the structure of frataxin that is recognized by ISU. Holo frataxin is also shown to mediate the transfer of iron from holo frataxin to nucleation sites for [2Fe-2S] cluster formation on ISU. We have demonstrated elsewhere [J. Am. Chem. Soc. 2002, 124, 8774-8775] that this iron-bound form of ISU is viable for assembly of holo ISU, either by subsequent addition of sulfide or by NifS-mediated sulfur delivery. Provision of holo frataxin and inorganic sulfide is sufficient for cluster assembly in up to 70% yield. With NifS as a sulfur donor, yields in excess of 70% of holo ISU were obtained. Both UV-vis and CD spectroscopic characteristics were found to be consistent with those of previously characterized ISU proteins. The time course for cluster assembly was monitored from the 456 nm absorbance of holo ISU formed during the [2Fe-2S] cluster assembly reaction. A kinetic rate constant k(obs) approximately 0.075 min(-)(1) was determined with 100 microM ISU, 2.4 mM Na(2)S, and 40 microM holo frataxin in 50 mM Tris-HCl (pH 7.5) with 4.3 mM DTT. Similar rates were obtained for NifS-mediated sulfur delivery, consistent with iron release from frataxin as a rate-limiting step in the cluster assembly reaction.

Escherichia coli↗
PubMed2005

The role of diisopropanolamine (dipaH3) in cluster dimerisation and polymerisation: from spin frustrated S= 5 FeIII 6 clusters to the novel 1-D covalent polymer of mixed valence [CoII3CoIII] tetramers.

The synthesis, crystal structures and magnetic properties of two hexanuclear Fe(6) clusters of general formula [Fe(6)(O)(2)(OH)(2)(O(2)CR)(10)(dipaH(2))(2)].xMeCN.yH(2)O (R = Ph, x= 5.5, y= 1 (1), R = C(Me)(3), x= 2, y= 3 (2)) are reported. The presence of the flexible amino-alcohol ligand diisopropanolamine (dipaH(3)) induces the dimerisation of two trinuclear Fe(III) complexes, [Fe(3)O(O(2)CPh)(6)(H(2)O)(3)](NO(3)) and [Fe(3)O(O(2)CC(Me)(3))(6)(H(2)O)(3)](O(2)CC(Me)(3)), to form the hexanuclear clusters 1 and 2. DC magnetic susceptibility measurements on 1 and 2 assign ground spin states of S= 5, with zero-field splitting parameters (D) of ca. 0.25 cm(-1) obtained from magnetisation isotherms. AC susceptibilities showed no maxima as a function of frequency, at low temperatures, and this confirmed the lack of single-molecule magnetic behaviour. Clusters 1 and 2 are isostructural, consisting of two fused {Fe(3)O} trinuclear units, bridged in two positions by one mu(2)-OH(-) unit and two mu(2)-O(2)CR(-) bridging carboxylates (R = Ph (), C(Me)(3)()). The two singly deprotonated dipaH(2)(-) bridging ligands span the Fe1-Fe2 edges in and via one micro(2)-bridging alcohol arm and one terminal nitrogen atom while the second alcohol arm remains free. The ground spin state of S= 5 in 1 and 2 can be attributed to the presence of spin frustration within the system. 1 and 2 join a small family of spin frustrated S= 5 Fe(6) systems the magnetism of which give weight to a recent report that it is the trans position of the two shortest Fe(2) pair frustrated exchange pathways in these Fe(6) clusters that gives rise to a ground spin state of S= 5 (trans) and not a ground spin state of S= 0 (cis). The Mössbauer spectra of 1 and 2 show two quadrupole doublets, as expected, at 295 K, but a broad asymmetric lineshape at 77 K. The synthesis and magnetic properties of {[Co(II)(3)Co(III)(OH)(O(2)CC(Me)(3))(4)(HO(2)CC(Me)(3))(2)(dipaH)(2)].2MeCN}(n)(3) are reported. 3 is a covalently bonded 1D polymer of tetrameric cobalt clusters. The presence of the dipaH(3) ligand here not only dimerises the [Co(II)(2)(micro-H(2)O)(O(2)CC(Me)(3))(4)(HO(2)CC(Me)(3))(4)] starting complex into the tetranuclear species but also polymerises the [Co(II)(3)Co(III)] clusters in 3 by acting as the propagating ligand in the 1D chain. Magnetic susceptibility measurements on show each [Co(4)] moiety exhibits weak antiferromagnetic coupling between the three Co(II)S= 3/2 metal centres and fitted J values are given. The ambiguity in assignment of the spin ground state of S= 1/2 or 3/2 is discussed.

Journal Article↗
PubMed2004

Mass-fractal clustering and power-law decay of cluster size in 1-propanol aqueous solution.

Mesoscale structure of 1-propanol aqueous solutions with propanol mole fraction xp ranging from 0.1 to 0.33 has been studied by means of small angle neutron scattering (SANS) and large-scale reverse Monte Carlo (RMC) technique. Analysis of the SANS intensities in terms of a fractal model shows that the fractal dimension df of mesoscale structure of the solution is about 1.8-1.9 for water-rich solution and about 1.5 for propanol-rich solution. Percolation analysis on the RMC results reveals that the water molecules and the propanol molecules cluster, respectively, as a mass fractal, the dimension dM of which is about 2.3-2.5 for both clusters for water-rich solution. Furthermore, the distribution of the cluster size is expressed by a simple power law with an exponent tau of about 1.35-1.5 for the propanol clusters and 1.05-1.2 for the water clusters. These results imply that the current solution is characterized by polydisperse mass fractals. In fact, a theoretical relation for polydisperse system of mass fractals, df = dM(2-tau), holds well in the current solution. The characteristic change in df from 1.8-1.9 to 1.5 described above is attributed to the crossover between the water-rich regime and the propanol-rich regime. Most of the water molecules and the propanol molecules are located on the interface between clusters, and the water molecules form thin layers of about 10 A thick irrespective of 1-propanol content studied.

Journal Article↗
PubMed2004

Statistical evaporation of rotating clusters. IV. Alignment effects in the dissociation of nonspherical clusters.

Unimolecular evaporation in rotating, nonspherical atomic clusters is investigated using phase space theory in its orbiting transition state version. The distributions of the total kinetic energy release epsilon(tr) and the rotational angular momentum J(r) are calculated for oblate top and prolate top main products with an arbitrary degree of deformation. The orientation of the angular momentum of the product cluster with respect to the cluster symmetry axis has also been obtained. This statistical approach is tested in the case of the small eight-atom Lennard-Jones cluster, for which comparison with extensive molecular dynamics simulations is presented. The role of the cluster shape has been systematically studied for larger, model clusters in the harmonic approximation for the vibrational densities of states. We find that the type of deformation (prolate versus oblate) plays little role on the distributions and averages of epsilon(tr) and J(r) except at low initial angular momentum. However, alignment effects between the product angular momentum and the symmetry axis are found to be significant, and maximum at some degree of oblateness. The effects of deformation on the rotational cooling and heating effects are also illustrated.

Journal Article↗
PubMed2006

The properties of ion-water clusters. II. Solvation structures of Na+, Cl-, and H+ clusters as a function of temperature.

Ion-water-cluster properties are investigated both through the multistate empirical valence bond potential and a polarizable model. Equilibrium properties of the ion-water clusters H+(H2O)100, Na+(H2O)100, Na+(H2O)20, and Cl-(H2O)17 in the temperature region 100-450 K are explored using a hybrid parallel basin-hopping and tempering algorithm. The effect of the solid-liquid phase transition in both caloric curves and structural distribution functions is investigated. It is found that sodium and chloride ions largely reside on the surface of water clusters below the cluster melting temperature but are solvated into the interior of the cluster above the melting temperature, while the solvated proton was found to have significant propensity to reside on or near the surface in both the liquid- and solid-state clusters.

Algorithms↗