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PubMed2006

Structures and relative stability of medium-sized silicon clusters. IV. Motif-based low-lying clusters Si21-Si30.

Structures and relative stability of four families of low-lying silicon clusters in the size range of Sin(n=21-30) are studied, wherein two families of the clusters show prolate structures while the third one shows near-spherical structures. The prolate clusters in the first family can be assembled by connecting two small-sized magic clusters Sin (n=6, 7, 9, or 10) via a fused-puckered-hexagonal-ring Si9 unit (a fragment of bulk diamond silicon), while those in the second family can be constructed on the basis of a structural motif consisting of a puckered-hexagonal-ring Si6 unit (also a fragment of bulk diamond silicon) and a small-sized magic cluster Sin (n=6, 7, 9, or 10). For Si21-Si29, the predicted lowest-energy clusters (except Si27) exhibit prolate structures. For clusters larger than Si25, the third family of near-spherical clusters becomes energetically competitive. These near-spherical clusters all exhibit endohedral cagedlike structures, and the cages are mostly homologue to the carbon-fullerene cages which consist of pentagons and hexagons exclusively. In addition, for Si26-Si30, we construct a new (fourth) family of low-lying clusters which have "Y-shaped" three-arm structures, where each arm is a small-sized magic cluster (Si6, Si7, or Si10). Density-functional calculation with the B3LYP functional shows that this new family of clusters is also energetically competitive, compared to the two prolate and one near-spherical low-lying families.

Journal Article↗
PubMed1998

Assembly of iron-sulfur clusters. Identification of an iscSUA-hscBA-fdx gene cluster from Azotobacter vinelandii.

An enzyme having the same L-cysteine desulfurization activity previously described for the NifS protein was purified from a strain of Azotobacter vinelandii deleted for the nifS gene. This protein was designated IscS to indicate its proposed role in iron-sulfur cluster assembly. Like NifS, IscS is a pyridoxal-phosphate containing homodimer. Information gained from microsequencing of oligopeptides obtained by tryptic digestion of purified IscS was used to design a strategy for isolation and DNA sequence analysis of a 7,886-base pair A. vinelandii genomic segment that includes the iscS gene. The iscS gene is contained within a gene cluster that includes homologs to nifU and another gene contained within the major nif cluster of A. vinelandii previously designated orf6. These genes have been designated iscU and iscA, respectively. Information available from complete genome sequences of Escherichia coli and Hemophilus influenzae reveals that they also encode iscSUA gene clusters. A wide conservation of iscSUA genes in nature and evidence that NifU and NifS participate in the mobilization of iron and sulfur for nitrogenase-specific iron-sulfur cluster formation suggest that the products of the iscSUA genes could play a general role in the formation or repair of iron-sulfur clusters. The proposal that IscS is involved in mobilization of sulfur for iron-sulfur cluster formation in A. vinelandii is supported by the presence of a cysE-like homolog in another gene cluster located immediately upstream from the one containing the iscSUA genes. O-Acetylserine synthase is the product of the cysE gene, and it catalyzes the rate-limiting step in cysteine biosynthesis. A similar cysE-like gene is also located within the nif gene cluster of A. vinelandii. The likely role of such cysE-like gene products is to increase the cysteine pool needed for iron-sulfur cluster formation. Another feature of the iscSUA gene cluster region from A. vinelandii is that E. coli genes previously designated as hscB, hscA, and fdx are located immediately downstream from, and are probably co-transcribed with, the iscSUA genes. The hscB, hscA, and fdx genes are also located adjacent to the iscSUA genes in both E. coli and H. influenzae. The E. coli hscA and hscB gene products have previously been shown to bear primary sequence identity when respectively compared with the dnaK and dnaJ gene products and have been proposed to be members of a heat-shock-cognate molecular chaperone system of unknown function. The close proximity and apparent co-expression of iscSUA and hscBA in A. vinelandii indicate that the proposed chaperone function of the hscBA gene products could be related to the maturation of iron-sulfur cluster-containing proteins. Attempts to place non-polar insertion mutations within either A. vinelandii iscS or hscA revealed that such mutations could not be stably maintained in the absence of the corresponding wild-type allele. These results reveal a very strong selective pressure against the maintenance of A. vinelandii iscS or hscA knock-out mutations and suggest that such mutations are either lethal or highly deleterious. In contrast to iscS or hscA, a strain having a polar insertion mutation within the cysE-like gene was readily isolated and could be stably maintained. These results show that the cysE-like gene located upstream from iscS is not essential for cell growth and that the cysE-like gene and the iscSUA-hscBA-fdx genes are contained within separate transcription units.

Amino Acid Sequence↗
PubMed2003

Characterization of cluster N5 as a fast-relaxing [4Fe-4S] cluster in the Nqo3 subunit of the proton-translocating NADH-ubiquinone oxidoreductase from Paracoccus denitrificans.

The NADH-quinone oxidoreductase from Paracoccus denitrificans consists of 14 subunits (Nqo1-14) and contains one FMN and eight iron-sulfur clusters. The Nqo3 subunit possesses fully conserved 11 Cys and 1 His in its N-terminal region and is considered to harbor three iron-sulfur clusters; however, only one binuclear (N1b) and one tetranuclear (N4) were previously identified. In this study, the Nqo3 subunit containing 1x[2Fe-2S] and 2x[4Fe-4S] clusters was expressed in Escherichia coli. The second [4Fe-4S](1+) cluster is detected by EPR spectroscopy below 6 K, exhibiting very fast spin relaxation. The resolved EPR spectrum of this cluster is broad and nearly axial. The subunit exhibits an absorption-type EPR signal around g approximately 5 region below 6 K, most likely arising from an S = 3/2 ground state of the fast-relaxing [4Fe-4S](1+) species. The substitution of the conserved His(106) with Cys specifically affected the fast-relaxing [4Fe-4S](1+) cluster, suggesting that this cluster is coordinated by His(106). In the cholate-treated NDH-1-enriched P. denitrificans membranes, we observed EPR signals arising from a [4Fe-4S] cluster below 6 K, exhibiting properties similar to those of cluster N5 detected in other complex I/NDH-1 and of the fast-relaxing [4Fe-4S](1+) cluster in the expressed Nqo3 subunit. Hence, we propose that the His-coordinated [4Fe-4S] cluster corresponds to cluster N5.

Amino Acid Sequence↗
PubMed1999

Functional assignment of the ORF2-iscS-iscU-iscA-hscB-hscA-fdx-ORF3 gene cluster involved in the assembly of Fe-S clusters in Escherichia coli.

Fe-S cluster, the nonheme-iron cofactor essential for the activity of many proteins, is incorporated into its target protein by an unknown mechanism. In Escherichia coli, genes in the ORF1-ORF2-iscS-iscU-iscA-hscB-hsc A-fdx-ORF3 cluster (the isc gene cluster) should be involved in the assembly of the Fe-S cluster since its coexpression with the reporter ferredoxin (Fd) dramatically increases the production of holoFd [Nakamura, M., Saeki, K., and Takahashi, Y. (1999) J. Biochem. 126, 10-18]. In this study we addressed the functional roles of the proteins encoded by the isc gene cluster with respect to the assembly of Fe-S clusters in four reporter Fds. Plasmids were constructed in which eight ORFs in the isc gene cluster were individually inactivated either by truncating the coding region or by introducing an oligonucleotide linker containing stop codons. By coexpressing these plasmids with reporter Fds, we show the iscS, iscA, hscA, and fdx genes to be required for the assembly of the Fe-S clusters. When these genes were absent from the coexpression plasmid, no overproduction was achieved in any reporter Fds examined. The inactivation of ORF2 and hscB had a partial but appreciable effect on the production of some Fds. Deletion of ORF1 produced no difference from the coexpression with the intact isc gene cluster. We also examined coexpression using the fdx gene in the isc gene cluster as a reporter Fd and identified iscS, hscB, hscA, and ORF3 as being involved in the assembly of the [2Fe-2S] cluster in this protein. We propose a model in which the fdx gene product functions as an intermediate site for Fe-S cluster assembly.

Amino Acid Sequence↗
PubMed2000

Cluster-cluster aggregation in binary mixtures

The structure and aggregation kinetics of three-dimensional clusters composed of two different monomeric species at three concentrations are thoroughly investigated by means of extensive, large-scale computer simulations. The aggregating monomers have all the same size and occupy the cells of a cubic lattice. Two bonding schemes are considered: (a) the binary diffusion-limited cluster-cluster aggregation (BDLCA) in which only the monomers of different species stick together, and (b) the invading binary diffusion-limited cluster-cluster aggregation (IBDLCA) in which additionally monomers of one of the two species are allowed to bond. In the two schemes, the mixed aggregates display self-similarity with a fractal dimension d(f) that depends on the relative molar fraction of the two species and on concentration. At a given concentration, when this molar fraction is small, d(f) approaches a value close to the reaction-limited cluster-cluster aggregation of one-component systems, and when the molar fraction is 0.5, d(f) becomes close to the value of the diffusion-limited cluster-cluster aggregation model. The crossover between these two regimes is due to a time-decreasing reaction probability between colliding particles, particularly at small molar fractions. Several dynamical quantities are studied as a function of time. The number of clusters and the weight-average cluster size display a power-law behavior only at small concentrations. The dynamical exponents are obtained for molar fractions above 0.3 but not at or below 0.2, indicating the presence of a critical transition between a gelling to a nongelling system. The cluster-size distribution function presents scaling for molar fractions larger than 0.2.

Journal Article↗
PubMed2007

Relative efficiency of unequal versus equal cluster sizes in cluster randomized and multicentre trials.

Cluster randomized and multicentre trials evaluate the effect of a treatment on persons nested within clusters, for instance, patients within clinics or pupils within schools. Optimal sample sizes at the cluster (centre) and person level have been derived under the restrictive assumption of equal sample sizes per cluster. This paper addresses the relative efficiency of unequal versus equal cluster sizes in case of cluster randomization and person randomization within clusters. Starting from maximum likelihood parameter estimation, the relative efficiency is investigated numerically for a range of cluster size distributions. An approximate formula is presented for computing the relative efficiency as a function of the mean and variance of cluster size and the intraclass correlation, which can be used for adjusting the sample size. The accuracy of this formula is checked against the numerical results and found to be quite good. It is concluded that the loss of efficiency due to variation of cluster sizes rarely exceeds 10 per cent and can be compensated by sampling 11 per cent more clusters.

Cluster Analysis↗
PubMed2006

Sample size for cluster randomized trials: effect of coefficient of variation of cluster size and analysis method.

BACKGROUND: Cluster randomized trials are increasingly popular. In many of these trials, cluster sizes are unequal. This can affect trial power, but standard sample size formulae for these trials ignore this. Previous studies addressing this issue have mostly focused on continuous outcomes or methods that are sometimes difficult to use in practice. METHODS: We show how a simple formula can be used to judge the possible effect of unequal cluster sizes for various types of analyses and both continuous and binary outcomes. We explore the practical estimation of the coefficient of variation of cluster size required in this formula and demonstrate the formula's performance for a hypothetical but typical trial randomizing UK general practices. RESULTS: The simple formula provides a good estimate of sample size requirements for trials analysed using cluster-level analyses weighting by cluster size and a conservative estimate for other types of analyses. For trials randomizing UK general practices the coefficient of variation of cluster size depends on variation in practice list size, variation in incidence or prevalence of the medical condition under examination, and practice and patient recruitment strategies, and for many trials is expected to be approximately 0.65. Individual-level analyses can be noticeably more efficient than some cluster-level analyses in this context. CONCLUSIONS: When the coefficient of variation is <0.23, the effect of adjustment for variable cluster size on sample size is negligible. Most trials randomizing UK general practices and many other cluster randomized trials should account for variable cluster size in their sample size calculations.

Cluster Analysis↗
PubMed1990

Responding to community-identified suicide clusters: statistical verification of the cluster is not the primary issue.

Establishing the presence of an epidemic is traditionally a first step in any outbreak investigation. For two reasons, however, this has not been a fruitful approach for suicide cluster investigations. First, the data necessary to statistically verify an excess number of suicidal incidents are often lacking or of poor quality. Second, and more important, when a community perceives that it is experiencing a suicide cluster, it is not immediately relevant whether the cluster is statistically significant. The perception of suicide clustering, and the highly charged emotional atmosphere associated with that perception, may dramatically heighten the potentially "contagious" effect of suicide. That the perception of clustering may itself be a risk factor for suicide distinguishes suicide clusters from all other clusters of fatal disease or illness. A community response plan should, therefore, be implemented to identify and refer persons who may be at high risk of suicide, regardless of whether the community-identified suicide cluster is statistically significant. Statistical techniques may be useful at several stages in the investigation and control of apparent suicide clusters, but statistical verification of a community-identified suicide cluster is not appropriate as a starting point for response to the cluster.

Adolescent↗
PubMed2002

Analysis of clustered binary outcomes using within-cluster paired resampling.

Conditional logistic regression (CLR) is useful for analyzing clustered binary outcome data when interest lies in estimating a cluster-specific exposure parameter while treating the dependency arising from random cluster effects as a nuisance. CLR aggregates unmeasured cluster-specific factors into a cluster-specific baseline risk and is invalid in the presence of unmodeled heterogeneous covariate effects or within-cluster dependency. We propose an alternative, resampling-based method for analyzing clustered binary outcome data, within-cluster paired resampling (WCPR), which allows for within-cluster dependency not solely due to baseline heterogeneity. For example, dependency may be in part caused by heterogeneity in response to an exposure across clusters due to unmeasured cofactors. When both CLR and WCPR are valid, our simulations suggest that the two methods perform comparably. When CLR is invalid, WCPR continues to have good operating characteristics. For illustration, we apply both WCPR and CLR to a periodontal data set where there is heterogeneity in response to exposure across clusters.

Adult↗
PubMed2002

Iron-sulfur cluster biosynthesis. Kinetic analysis of [2Fe-2S] cluster transfer from holo ISU to apo Fd: role of redox chemistry and a conserved aspartate.

ISU-type proteins mediate cluster transfer to apo protein targets. Rate constants have been determined for cluster transfer from ISU to apo Fd for both Homo sapiens and Schizosaccharomyces pombe proteins, and cross reactions have also been examined. Substitution of a key aspartate residue of ISU is found to decrease the rate of cluster transfer by at least an order of magnitude (for wild-type Hs ISU cluster transfer to Hs apo Fd, k(2) approximately 540 M(-1) min(-1), relative 56 M(-1) min(-1) for D37A ISU). This change in rate constant does not reflect any change in binding affinity of the ISU and Fd proteins. The pH dependencies of cluster transfer rates are similar for WT and D37A ISU, arguing against a role for Asp37 as a catalytic base, although evidence for general base catalysis mediating deprotonation of Cys from the apo target is supported by an observed pK(a) of 6.9 determined from the pH profiles for both WT and D37A ISU. Such a pK(a) value is at the lower limit for Cys and is common for solvent-accessible Cys thiols. The temperature dependence of the rate constant defining the cluster transfer reaction for wild type versus the aspartate derivative is distinct. Thermal activation parameters (DeltaH and DeltaS) are consistent with a solvent-accessible ISU-bound cluster, with desolvation as a principle barrier to cluster transfer. Experiments to determine the dependence of reaction rate constants on viscosity indicate cluster transfer to be rate-limiting. Fully oxidized cluster appears to be the natural state for transfer to target proteins. Reduced Fd does not readily reduce ISU-bound [2Fe-2S](2+) and does not promote cluster transfer to an apo Fd target.

Apoproteins↗
PubMed2003

Cluster-to-metal magnetic coupling: synthesis and characterization of 25-electron [Re6-nOsnSe8(CN)6](5-n)-(n = 1, 2) clusters and (Re6-nOsnSe8[CNCu(Me6tren)]6)9+(n = 0, 1, 2) assemblies.

The first face-capped octahedral clusters with 25 metal-based valence electrons are shown to provide versatile building units capable of engaging in magnetic exchange coupling. Reactions of [Re(5)OsSe(8)Cl(6)](3-) and [Re(4)Os(2)Se(8)Cl(6)](2-) with NaCN in a melt of NaNO(3) or KCF(3)SO(3) afford the 24-electron clusters [Re(5)OsSe(8)(CN)(6)](3-) and [Re(4)Os(2)Se(8)(CN)(6)](2-). The 13C NMR spectrum of a 13C-labeled version of the latter species indicates a 1:2 mixture of cis and trans isomers. Cyclic voltammograms of the clusters in acetonitrile display reversible [Re(5)OsSe(8)(CN)(6)](3-/4-), cis-[Re(4)Os(2)Se(8)(CN)(6)](2-/3-), and trans-[Re(4)Os(2)Se(8)(CN)(6)](2-/3-) couples at E(1/2) = -1.843, -0.760, and -1.031 V vs FeCp(2)(0/+), respectively, in addition to other redox processes. Accordingly, reduction of [Re(5)OsSe(8)(CN)(6)](3-) with sodium amalgam and [Re(4)Os(2)Se(8)(CN)(6)](2-) with cobaltocene produces the 25-electron clusters [Re(5)OsSe(8)(CN)(6)](4-) and [Re(4)Os(2)Se(8)(CN)(6)](3-). EPR spectra of these S = 1/2 species in frozen DMF solutions exhibit isotropic signals with g = 1.46 for the monoosmium cluster and g = 1.74 and 1.09 for the respective cis and trans isomers of the diosmium cluster. In each case, results from DFT calculations show the unpaired spin to delocalize to some extent into the pi* orbitals of the cyanide ligands, suggesting the possibility of magnetic superexchange. Reaction of [Re(5)OsSe(8)(CN)(6)](3-) with [Ni(H(2)O)(6)](2+) in aqueous solution generates the porous Prussian blue analogue Ni(3)[Re(5)OsSe(8)(CN)(6)](2).32H(2)O; however, the tendency of the 25-electron clusters to oxidize in water prohibits their use in reactions of this type. Instead, a series of cyano-bridged assemblies, [Re(6-n)Os(n)Se(8)[CNCu(Me(6)tren)](6)](9+) (n = 0, 1, 2; Me(6)tren = tris(2-(dimethylamino)ethyl)amine), were synthesized to permit comparison of the exchange coupling abilities of clusters with 23-25 electrons. As expected, the results of magnetic susceptibility measurements show no evidence for exchange coupling in the assemblies containing the 23- and 24-electron clusters, but reveal the presence of weak ferromagnetic coupling in [Re(4)Os(2)Se(8)[CNCu(Me(6)tren)](6)](9+). Assuming all cluster-Cu(II) exchange interactions to be equivalent, the data were fit to give an estimated coupling strength of J = 0.4 cm(-1). To our knowledge, the ability of such clusters to participate in magnetic exchange coupling has never previously been demonstrated.

Journal Article↗
PubMed1998

The ParaHox gene cluster is an evolutionary sister of the Hox gene cluster.

Genes of the Hox cluster are restricted to the animal kingdom and play a central role in axial patterning in divergent animal phyla. Despite its evolutionary and developmental significance, the origin of the Hox gene cluster is obscure. The consensus is that a primordial Hox cluster arose by tandem gene duplication close to animal origins. Several homeobox genes with high sequence identity to Hox genes are found outside the Hox cluster and are known as 'dispersed' Hox-like genes; these genes may have been transposed away from an expanding cluster. Here we show that three of these dispersed homeobox genes form a novel gene cluster in the cephalochordate amphioxus. We argue that this 'ParaHox' gene cluster is an ancient paralogue (evolutionary sister) of the Hox gene cluster; the two gene clusters arose by duplication of a ProtoHox gene cluster. Furthermore, we show that amphioxus ParaHox genes have co-linear developmental expression patterns in anterior, middle and posterior tissues. We propose that the origin of distinct Hox and ParaHox genes by gene-cluster duplication facilitated an increase in body complexity during the Cambrian explosion.

Amino Acid Sequence↗
PubMed2006

Special stability of cationic MPb12+ clusters and superalkali character of neutral MPb12 clusters (M = B, Al, Ga, In, and Tl).

The electronic structures and stabilities of cationic MPb12+ clusters (M = B, Al, Ga, In, and Tl) with 50 valence electrons are investigated within density functional theory. It is shown that, at the B3LYP/cc-pVDZ(-PP) and BPW91/cc-pVDZ(-PP) levels of theory, the structures of MPb12+ with icosahedra (I(h)) symmetry are energetically favorable, and their high stabilities may arise from the closed-shell nature of the pi subsystems which are subject to the 2(N(pi + 1)2 rule with N(pi = 1). In addition, the possessing of large nucleus-independent chemical shifts of the five kinds of clusters reflects the common aromatic character of these clusters. From the comparison of our studies on the binding energies and the highest occupied molecular orbital and the lowest unoccupied molecular orbital energy gaps, the cluster AlPb12+ has higher stability than the others and this is consistent with the recent mass-spectrometric discovery of Al-doped Pb(n)+ clusters, in which AlPb12+ is highly abundant. The same methods are used to search for the structures of the neutral MPb12 clusters. The calculations reveal that the most stable geometries of the BPb12 and GaPb12 clusters have I(h) symmetry, the AlPb12 and InPb12 clusters have T(h) symmetry, and the TlPb12 cluster has C5v symmetry. Furthermore, the vertical ionization potentials of the neutral MPb12 clusters are smaller than that of some alkali atoms, indicating that the neutral MPb12 clusters possess superalkali character.

Journal Article↗
PubMed2002

Molecular cloning and expression of mouse Wnt14, and structural comparison between mouse Wnt14-Wnt3a gene cluster and human WNT14-WNT3A gene cluster.

Glycoprotein WNTs play key roles in carcinogenesis and embryogenesis. Human WNT14 and WNT3A genes are clustered in human chromosome 1q42 region with an interval of about 58 kb. Here, mouse Wnt14 was isolated to compare the structure of human WNT14-WNT3A gene cluster with that of mouse Wnt14-Wnt3a gene cluster. Mouse Wnt14 showed 98.1% total-amino-acid identity with human WNT14, and 61.9% total-amino-acid identity with human WNT14B/WNT15. Mouse Wnt14 mRNA was expressed in adult brain, lung, skeletal muscle, heart, and 17-day embryo. Mouse Wnt14 and Wnt3a genes were clustered in head-to-head manner with an interval of about 16 kb. Exon-intron structures were well conserved between human WNT14-WNT3A gene cluster and mouse Wnt14-Wnt3a gene cluster. Capicua-related sequence and AK024248-related sequence were identified in the intergenic region of human Wnt14-Wnt3a gene cluster as well as in other human chromosomal loci, but not in that of mouse Wnt14-Wnt3a gene cluster. Capicua-related sequences were pseudogenes derived from Capicua gene on human chromosome 19q13. Capicua pseudogene and AK024248-related sequence were clustered in tail-to-tail manner with interval ranging from 2.2 to 11.0 kb. AK024248-related sequences in several human genome draft sequences were truncated in the 3'-portion compared with that in the intergenic region of human WNT14-WNT3A gene cluster. This is the first report on structural comparison of WNT gene clusters in human genome and in mouse genome.

Amino Acid Sequence↗
PubMed2026

Motif-Cluster: Motif driven prioritization of transcription factor binding clusters.

Genome-wide analyses of transcription factor (TF) motif binding sites have largely emphasized individual high-affinity sites, while overlooking the regulatory importance of locally repetitive motif clusters. Such clusters, including combinations of weak and strong binding sites, can collectively enhance TF occupancy and regulatory activity. Here we present Motif-Cluster, an open-source framework for motif-driven prioritization and visualization of TF binding clusters using sequence information alone. Motif-Cluster integrates a density-based clustering strategy with flexible modeling of binding-site gaps and affinity signals, enabling the identification and ranking of candidate regulatory regions without requiring experimental binding data. Through simulations and multiple real-data analyses, we show that combining gap distributions with binding affinity effectively balances cluster size and signal strength while reducing noise from weak sites. Application to ZNF410 successfully recovers the previously characterized binding clusters in the CHD4 promoter, which are conserved between human and mouse. Additional case studies involving PHB1, TWIST1, and EGR1 further demonstrate the general applicability of the method across diverse transcription factors. Motif-Cluster also provides intuitive visualization and reproducible workflows to facilitate interpretation of spatially dense motif patterns. Overall, Motif-Cluster offers a robust and flexible approach for prioritizing transcription factor regulatory regions from genome-wide motif scans, enabling biological discovery and guiding experimental design, particularly in settings where direct genome-wide binding assays are unavailable.

Transcription Factors↗
PubMed2001

Analysis of temporal gene expression profiles: clustering by simulated annealing and determining the optimal number of clusters.

MOTIVATION: Cluster analysis of genome-wide expression data from DNA microarray hybridization studies has proved to be a useful tool for identifying biologically relevant groupings of genes and samples. In the present paper, we focus on several important issues related to clustering algorithms that have not yet been fully studied. RESULTS: We describe a simple and robust algorithm for the clustering of temporal gene expression profiles that is based on the simulated annealing procedure. In general, this algorithm guarantees to eventually find the globally optimal distribution of genes over clusters. We introduce an iterative scheme that serves to evaluate quantitatively the optimal number of clusters for each specific data set. The scheme is based on standard approaches used in regular statistical tests. The basic idea is to organize the search of the optimal number of clusters simultaneously with the optimization of the distribution of genes over clusters. The efficiency of the proposed algorithm has been evaluated by means of a reverse engineering experiment, that is, a situation in which the correct distribution of genes over clusters is known a priori. The employment of this statistically rigorous test has shown that our algorithm places greater than 90% genes into correct clusters. Finally, the algorithm has been tested on real gene expression data (expression changes during yeast cell cycle) for which the fundamental patterns of gene expression and the assignment of genes to clusters are well understood from numerous previous studies.

Algorithms↗
PubMed2001

Cluster headache in women: clinical characteristics and comparison with cluster headache in men.

OBJECTIVE: To study the clinical characteristics of cluster headache in women. Cluster headache is a disorder of men (male to female ratio 6-7:1). METHODS: Retrospective chart review to identify all women diagnosed with cluster headache at an academic headache centre from January 1995 through July 1998. RESULTS: Thirty two women and 69 men were identified. The mean age of onset of cluster headache was 29.4 years in women versus 31.3 years in men. Two peaks of onset in women (2nd and 5th decade) were identified compared with one in men (3rd decade). Episodic cluster headache was present in 75% of women and 77% of men. Women and men had on average 3 attacks a day, but attack duration was shorter in women (67.2 minutes v 88.2 minutes). Cluster headache period duration (11.1 weeks v 10 weeks) and remission periods (21.1 months v 23.1 months) were similar in women and men. Miosis and ptosis seemed to be less common in women (miosis 13.3% v 24.6%, ptosis 41.9% v 58.1%) whereas lacrimation and nasal congestion/rhinorrhoea were almost equally prevalent in women and men. Women had more nausea than men (62.5% v 43.5%, p=0.09) and significantly more vomiting (46.9% v 17.4%, p=0.003). Photophobia occurred in 75% of women and 81.2% of men, and phonophobia occurred in 50% of women and 47.8% of men. CONCLUSIONS: The clinical characteristics of cluster headache in women are very similar to those in men. Women develop the disorder at an earlier age of onset and experience more "migrainous symptoms" with cluster headache, especially vomiting. Both men and women have frequent photophobia and phonophobia with cluster headache attacks. These symptoms are not included in the International Headache Society cluster headache criteria, suggesting the need for possible criteria revision.

Adult↗
PubMed2006

Planning a cluster randomized trial with unequal cluster sizes: practical issues involving continuous outcomes.

BACKGROUND: Cluster randomization design is increasingly used for the evaluation of health-care, screening or educational interventions. At the planning stage, sample size calculations usually consider an average cluster size without taking into account any potential imbalance in cluster size. However, there may exist high discrepancies in cluster sizes. METHODS: We performed simulations to study the impact of an imbalance in cluster size on power. We determined by simulations to which extent four methods proposed to adapt the sample size calculations to a pre-specified imbalance in cluster size could lead to adequately powered trials. RESULTS: We showed that an imbalance in cluster size can be of high influence on the power in the case of severe imbalance, particularly if the number of clusters is low and/or the intraclass correlation coefficient is high. In the case of a severe imbalance, our simulations confirmed that the minimum variance weights correction of the variation inflaction factor (VIF) used in the sample size calculations has the best properties. CONCLUSION: Publication of cluster sizes is important to assess the real power of the trial which was conducted and to help designing future trials. We derived an adaptation of the VIF from the minimum variance weights correction to be used in case the imbalance can be a priori formulated such as "a proportion (gamma) of clusters actually recruit a proportion (tau) of subjects to be included (gamma < or = tau)".

Analysis of Variance↗