Sample Size Estimation in Cluster Randomized Studies with Varying Cluster Size

Cluster randomized studies are common in community trials. The standard method for estimating sample size for cluster randomized studies assumes a common cluster size. However often in cluster randomized studies, size of the clusters vary. In this paper, we derive sample size estimation for continuous outcomes for cluster randomized studies while accounting for the variability due to cluster size. It is shown that the proposed formula for estimating total cluster size can be obtained by adding a correction term to the traditional formula which uses the average cluster size. Application of these results to the design of a health promotion educational intervention study is discussed.     

Power calculation for cross-sectional stepped wedge cluster randomized trials with variable cluster sizes

Standard sample size calculation formulas for stepped wedge cluster randomized trials (SW-CRTs) assume that cluster sizes are equal. When cluster sizes vary substantially, ignoring this variation may lead to an under-powered study. We investigate the relative efficiency of a SW-CRT with varying cluster sizes to equal cluster sizes, and derive variance estimators for the intervention effect that account for this variation under a mixed effects model—a commonly used approach for analyzing data from cluster randomized trials. When cluster sizes vary, the power of a SW-CRT depends on the order in which clusters receive the intervention, which is determined through randomization. We first derive a variance formula that corresponds to any particular realization of the randomized sequence and propose efficient algorithms to identify upper and lower bounds of the power. We then obtain an “expected” power based on a first-order approximation to the variance formula, where the expectation is taken with respect to all possible randomization sequences. Finally, we provide a variance formula for more general settings where only the cluster size arithmetic mean and coefficient of variation, instead of exact cluster sizes, are known in the design stage. We evaluate our methods through simulations and illustrate that the average power of a SW-CRT decreases as the variation in cluster sizes increases, and the impact is largest when the number of clusters is small.     

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.     

Iron-sulfur cluster biosynthesis. Molecular chaperone DnaK promotes IscU-bound [2Fe-2S] cluster stability and inhibits cluster transfer activity

IscU functions as a scaffold for Fe-S cluster assembly and transfer, and is known to be a substrate protein for molecular chaperones. Kinetic studies of Fe-S cluster transfer from holo IscU to apo Fd in the presence of chaperone DnaK demonstrate an inhibitory effect on the rate of Fe-S cluster transfer from IscU. Binding of DnaK reduces the rate of formation of the IscU-Fd complex (greater than 8-fold), but has little influence on the intrinsic rate of iron-sulfur cluster transfer to apo Fd. Apparently the molecular chaperone DnaK does not facilitate the process of Fe-S cluster transfer from IscU. Rather, DnaK has a modest influence on the stability of the IscU-bound Fe-S cluster that may reflect a more important role in promoting cluster assembly. In accord with prior observations the cochaperone DnaJ stimulates the ATPase activity of DnaK, but has a minimal influence on IscU cluster transfer activity, either alone or in concert with DnaK.     

Iron–sulfur cluster exchange reactions mediated by the human Nfu protein

Human Nfu is an iron–sulfur cluster protein that has recently been implicated in multiple mitochondrial dysfunctional syndrome (MMDS1). The Nfu family of proteins shares a highly homologous domain that contains a conserved active site consisting of a CXXC motif. There is less functional conservation between bacterial and human Nfu proteins, particularly concerning their Iron–sulfur cluster binding and transfer roles. Herein, we characterize the cluster exchange chemistry of human Nfu and its capacity to bind and transfer a [2Fe–2S] cluster. The mechanism of cluster uptake from a physiologically relevant [2Fe–2S](GS)₄ cluster complex, and extraction of the Nfu-bound iron–sulfur cluster by glutathione are described. Human holo Nfu shows a dimer-tetramer equilibrium with a protein to cluster ratio of 2:1, reflecting the Nfu-bridging [2Fe–2S] cluster. This cluster can be transferred to apo human ferredoxins at relatively fast rates, demonstrating a direct role for human Nfu in the process of [2Fe–2S] cluster trafficking and delivery.     

The SYSTERS protein sequence cluster set

The SYSTERS (short for SYSTEmatic Re-Searching) protein sequence cluster set consists of the classification of all sequences from SWISS-PROT and PIR into disjoint protein family clusters and hierarchically into superfamily and subfamily clusters. The cluster set can be searched with a sequence using the SSMAL search tool or a traditional database search tool like BLAST or FASTA. Additionally a multiple alignment is generated for each cluster and annotated with domain information from the Pfam database of protein domain families. A taxonomic overview of the organisms covered by a cluster is given based on the NCBI taxonomy. The cluster set is available for querying and browsing at http://www.dkfz-heidelberg. de/tbi/services/cluster/systersform     

Glutathione-complexed [2Fe-2S] clusters function in Fe–S cluster storage and trafficking

Glutathione-coordinated [2Fe-2S] complex is a non-protein-bound [2Fe-2S] cluster that is capable of reconstituting the human iron-sulfur cluster scaffold protein IscU. This complex demonstrates physiologically relevant solution chemistry and is a viable substrate for iron-sulfur cluster transport by Atm1p exporter protein. Herein, we report on some of the possible functional and physiological roles for this novel [2Fe-2S](GS₄) complex in iron-sulfur cluster biosynthesis and quantitatively characterize its role in the broader network of Fe–S cluster transfer reactions. UV–vis and circular dichroism spectroscopy have been used in kinetic studies to determine second-order rate constants for [2Fe-2S] cluster transfer from [2Fe-2S](GS₄) complex to acceptor proteins, such as human IscU, Schizosaccharomyces pombe Isa1, human and yeast glutaredoxins (human Grx2 and Saccharomyces cerevisiae Grx3), and human ferredoxins. Second-order rate constants for cluster extraction from these holo proteins were also determined by varying the concentration of glutathione, and a likely common mechanism for cluster uptake was determined by kinetic analysis. The results indicate that the [2Fe-2S](GS₄) complex is stable under physiological conditions, and demonstrates reversible cluster exchange with a wide range of Fe–S cluster proteins, thereby supporting a possible physiological role for such centers.     

Characterisation of oxidised 7Fe dicluster ferredoxins with NMR spectroscopy

Dicluster ferredoxins (Fds) from Sulfolobus acidocaldarius and Desulfovibrio africanus (FdIII) have been studied using 1H NMR. Both wild-type proteins contain a [3Fe-4S]+/0 and a [4Fe-4S]2+/+ cluster as isolated. The [4Fe-4S]2+/+ cluster (cluster II) is bound by cysteine residues arranged in a classic ferredoxin motif: CysI-(Xaa)2-CysII-(Xaa)2-CysIII-(Xaa)n-CysIV-Pro , whilst the binding motif of the [3Fe-4S]+/0 cluster (cluster I) has a non-ligating aspartic acid (Asp14) at position II, i.e. CysI-(Xaa)2-Asp-(Xaa)2-CysIII. D. africanus FdIII undergoes facile cluster transformation from the 7Fe form to the 8Fe form, but S. acidocaldarius Fd does not. Many factors determine the propensity of a cluster to undergo interconversion, including the presence, and correct orientation, of a suitable ligand. We have investigated this using 1H NMR by introducing a potential fourth ligand into the binding motif of cluster I of D. africanus FdIII. Asp14 has been mutated to cysteine (D14C), glutamic acid (D14E) and histidine (D14H). Cluster incorporation was performed in vitro. The cluster types present were identified from the chemical shift patterns and temperature-dependent behaviour of the hyperfine-shifted resonances. Factors influencing cluster ligation and cluster interconversion, in vitro, are discussed. Furthermore, the data have established that the residue at position II in the cluster binding motif of cluster I is influential in determining the chemical shift pattern observed for a [3Fe-4S]+ cluster when a short/symmetric binding motif is present. Based on this, a series of rules for characterising the 1H NMR chemical shifts of mono- and di-cluster [3Fe-4S]+ cluster-containing ferredoxins is given.     

Factors affecting formation of cluster roots in Myrica gale seedlings in water culture

The effect of nutrient deficiency, aeration, phosphorus supply, and nitrogen source on the formation of cluster (proteoid) roots was examined in Myrica gale seedlings growing in water culture. Only the omission of phosphorus resulted in the formation of significant numbers to cluster roots when plants were grown in a number of 1/4 strength Hoagland's solutions, each lacking one mineral nutrient. Aeration shortened the time required for cluster root formation and increased the percentage of plants forming cluster roots. The proportion of the root system comprised of cluster roots decreased as the phosphorus concentration in the solution increased and no cluster roots formed in solutions containing 8 mg P/L. Phosphorus supply also affected total plant biomass, proportion of biomass comprising nitrogen-fixing nodules, shoot:root ratio, phosphorus concentration in the leaves and phosphorus content of the plants. The plants showed luxury consumption of phosphorus and were able to produce large amounts of biomass utilizing only stored phosphorus.Nitrogen source also affected cluster root formation. Urea-fed plants produced cluster roots more quickly and devoted a substantially larger proportion of root growth to cluster roots than did nitrate-fed plants. The longest cluster root axes were produced in nitrate-fed plants supplied with no phosphorus and the shortest were in urea-fed plants at 4 mg P L^–1.Four methods for expressing the extent of cluster root formation were examined and it was concluded that cluster roots as a proportion of total fine root dry weight is preferable in many cases. Formation of cluster roots in response to phosphorus deficiency coupled with previously demonstrated traits allows Myrica gale to adapt to a wide range of soil conditions.     

A Cluster Operating System Supporting Parallel Computing

The single factor limiting the harnessing of the enormous computing power of clusters for parallel computing is the lack of appropriate software. Present cluster operating systems are not built to support parallel computing – they do not provide services to manage parallelism. The cluster operating environments that are used to assist the execution of parallel applications do not provide support for both Message Passing (MP) or Distributed Shared Memory (DSM) paradigms. They are only offered as separate components implemented at the user level as library and independent servers. Due to poor operating systems users must deal with computers of a cluster rather than to see this cluster as a single powerful computer. A Single System Image of the cluster is not offered to users. There is a need for an operating system for clusters. We claim and demonstrate that it is possible to develop a cluster operating system that is able to efficiently manage parallelism, support Message Passing and DSM and offer the Single System Image. In order to substantiate the claim the first version of a cluster operating system, called GENESIS, that manages parallelism and offers the Single System Image has been developed.     

Characterization of the cofactor composition of Escherichia coli biotin synthase

The cofactor content of in vivo, as-isolated, and reconstituted forms of recombinant Escherichia coli biotin synthase (BioB) has been investigated using the combination of UV-visible absorption, resonance Raman, and M?ssbauer spectroscopies along with parallel analytical and activity assays. In contrast to the recent report that E. coli BioB is a pyridoxal phosphate (PLP)-dependent enzyme with intrinsic cysteine desulfurase activity (Ollagnier-deChoudens, S., Mulliez, E., Hewitson, K. S., and Fontecave, M. (2002) Biochemistry 41, 9145-9152), no evidence for PLP binding or for PLP-induced cysteine desulfurase or biotin synthase activity was observed with any of the forms of BioB investigated in this work. The results confirm that BioB contains two distinct Fe-S cluster binding sites. One site accommodates a [2Fe-2S](2+) cluster with partial noncysteinyl ligation that can only be reconstituted in vitro in the presence of O(2). The other site accommodates a [4Fe-4S](2+,+) cluster that binds S-adenosylmethionine (SAM) at a unique Fe site of the [4Fe-4S](2+) cluster and undergoes O(2)-induced degradation via a distinct type of [2Fe-2S](2+) cluster intermediate. In vivo M?ssbauer studies show that recombinant BioB in anaerobically grown cells is expressed exclusively in an inactive form containing only the as-isolated [2Fe-2S](2+) cluster and demonstrate that the [2Fe-2S](2+) cluster is not a consequence of overexpressing the recombinant enzyme under aerobic growth conditions. Overall the results clarify the confusion in the literature concerning the Fe-S cluster composition and the in vitro reconstitution and O(2)-induced cluster transformations that are possible for recombinant BioB. In addition, they provide a firm foundation for assessing cluster transformations that occur during turnover and the catalytic competence of the [2Fe-2S](2+) cluster as the immediate S-donor for biotin biosynthesis.     

Mechanisms of redox-coupled proton transfer in proteins: role of the proximal proline in reactions of the [3Fe-4S] cluster in Azotobacter vinelandii ferredoxin I

The 7Fe ferredoxin from Azotobacter vinelandii (AvFdI) contains a [3Fe-4S](+/0) cluster that binds a single proton in its reduced level. Although the cluster is buried, and therefore inaccessible to solvent, proton transfer from solvent to the cluster is fast. The kinetics and energetics of the coupled electron-proton transfer reaction at the cluster have been analyzed in detail by protein-film voltammetry, to reveal that proton transfer is mediated by the mobile carboxylate of an adjacent surface residue, aspartate-15, the pK of which is sensitive to the charge on the cluster. This paper examines the role of a nearby proline residue, proline-50, in proton transfer and its coupling to electron transfer. In the P50A and P50G mutants, a water molecule has entered the cluster binding region; it is hydrogen bonded to the backbone amide of residue-50 and to the Asp-15 carboxylate, and it is approximately 4 A from the closest sulfur atom of the cluster. Despite the water molecule linking the cluster more directly to the solvent, proton transfer is not accelerated. A detailed analysis reveals that Asp-15 remains a central part of the mechanism. However, the electrostatic coupling between cluster and carboxylate is almost completely quenched, so that cluster reduction no longer induces such a favorable shift in the carboxylate pK, and protonation of the base no longer induces a significant shift in the pK of the cluster. The electrostatic coupling is crucial for maintaining the efficiency of proton transfer both to and from the cluster, over a range of pH values.     

Evolution of a 6-200 Mb long-range repeat cluster in the genus Mus

By fluorescence in situ hybridization, we mapped the location of genes associated with the Sp100-rs cluster, a long-range repeat cluster in chromosome 1 of the house mouse, Mus musculus. The cluster comprises between 60 and 2000 repeats and extends over 6-200 Mb of the M. musculus genome, depending on the source of the cluster. The cluster evolved during the last two million years in the genus Mus in the lineage to which M. musculus belongs. The Asiatic mouse species M. caroli is not in this lineage and does not possess the cluster. M. caroli represents the ancestral genomic organization of the cluster source components Sp100, Csprs and Ifi75: they are located close to each other in the same chromosome band (1D). However, Sp100-rs, the principal gene of the cluster, is not present in the M. caroli genome. It is a chimeric M. musculus gene that arose by fusion of Csprs and the 5' part of Sp100. Sp100-rs and Ifi75 are homogeneously distributed throughout the cluster while Sp100 and Csprs in its original sequence context flank the cluster on opposite sides. Our results suggest a model for the origin and evolution of the long-range repeat cluster by duplication, gene fusion and amplification.     

An SCI-Based PC Cluster Utilizing Coherent Network Cache

It is extremely important to minimize network access time in constructing a high-performance PC cluster system. For an SCI-based PC cluster, it is possible to reduce the network access time by maintaining network cache in each cluster node. This paper presents a Network-Cache-Coherent-NUMA (NCC-NUMA) card that utilizes network cache for SCI-based PC clustering. The NCC-NUMA card is directly plugged into the PCI slot of each node, and contains shared memory, network cache, and interconnection modules. The network cache is maintained for the shared memory on the PCI bus of cluster nodes. The coherency mechanism between the network cache and the shared memory is based on the IEEE SCI standard. Both a simulator and an NCC-NUMA prototype card are developed to evaluate the performance of the system. According to the experiments, the cluster system with the NCC-NUMA card showed considerable improvements compared with an SCI-based cluster without network cache.     

WWW access to the SYSTERS protein sequence cluster set

SUMMARY: We present a Web server where the SYSTERS cluster set of the non-redundant protein database consisting of sequences from SWISS-PROT and PIR is being made available for querying and browsing. The cluster set can be searched with a new sequence using the SSMAL search tool. Additionally, a multiple alignment is generated for each cluster and annotated with domain information from the Pfam protein family database. AVAILABILITY: The server address is http://www.dkfz-heidelberg.de/tbi/services/cluster/ systersform     

Revolving movement of a dynamic cluster of actin filaments during mitosis

The actin cytoskeleton undergoes rapid changes in its architecture during mitosis. Here, we demonstrate novel actin assembly dynamics in M phase. An amorphous cluster of actin filaments appears during prometaphase, revolves horizontally along the cell cortex at a constant angular speed, and fuses into the contractile ring after three to four revolutions. Cdk1 activity is required for the formation of this mitotic actin cluster and its revolving movement. Rapid turnover of actin in the filaments takes place everywhere in the cluster and is also required for its cluster rotation during mitosis. Knockdown of Arp3, a component of the actin filament-nucleating Arp2/3 complex, inhibits the formation of the mitotic actin cluster without affecting other actin structures. These results identify Arp2/3 complex as a key factor in the generation of the dynamic actin cluster during mitosis.     

Hox genes are not always Colinear

The deuterostomes are the clade of animals for which we have the most detailed understanding of Hox cluster organisation. With the Hox cluster of amphioxus (Branchiostoma floridae) we have the best prototypical, least derived Hox cluster for the group, whilst the urochordates present us with some of the most highly derived and disintegrated clusters. Combined with the detailed mechanistic understanding of vertebrate Hox regulation, the deuterostomes provide much of the most useful data for understanding Hox cluster evolution. Considering both the prototypical and derived deuterostome Hox clusters leads us to hypothesize that Temporal Colinearity is the main constraining force on Hox cluster organisation, but until we have a much deeper understanding of the mechanistic basis for this phenomenon, and know how widespread across the Bilateria the mechanism(s) is/are, then we cannot know how the Hox cluster of the last common bilaterian operated and what have been the major evolutionary forces operating upon the Hox gene cluster.