Splitting an Ordering into a Partition to Minimize Diameter

k consisting of k clusters, with k > 2. Bottom-up agglomerative approaches are also commonly used to construct partitions, and we discuss these in terms of worst-case performance for metric data sets. Our main contribution derives from a new restricted partition formulation that requires each cluster to be an interval of a given ordering of the objects being clustered. Dynamic programming can optimally split such an ordering into a partition P^k for a large class of objectives that includes min-diameter. We explore a variety of ordering heuristics and show that our algorithm, when combined with an appropriate ordering heuristic, outperforms traditional algorithms on both random and non-random data sets.     

For whom the bell tolls? DING proteins in health and disease

DING proteins, identified mainly by their eponymous N-terminal sequences, are ubiquitous in living organisms. Amongst bacteria, they are common in pseudomonads, and have been characterised with respect to genetics and structure. They form part of a wider family of phosphate-binding proteins, with emerging roles in phosphate acquisition and pathogenicity. Many DING proteins have been isolated in eukaryotes, in which they have been associated with very diverse biological activities, often in the context of possible signalling roles. Disease states in which DING proteins have been implicated include rheumatoid arthritis, lithiasis, atherosclerosis, some tumours and tumour-associated cachexia, and bacterial and viral adherence. Complete genetic and structural characterisation of eukaryotic DING genes and proteins is still lacking, though the phosphate-binding site seems to be conserved. Whether as bacterial proteins related to bacterial pathogenicity, or as eukaryotic components of biochemical signalling systems, DING proteins require further study. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Nucleation and growth mechanism of ferroelectric domain-wall motion

The motion of domain walls is critical to many applications involving ferroelectric materials, such as fast high-density non-volatile random access memory. In memories of this sort, storing a data bit means increasing the size of one polar region at the expense of another, and hence the movement of a domain wall separating these regions. Experimental measurements of domain growth rates in the well-established ferroelectrics PbTiO3 and BaTiO3 have been performed, but the development of new materials has been hampered by a lack of microscopic understanding of how domain walls move. Despite some success in interpreting domain-wall motion in terms of classical nucleation and growth models, these models were formulated without insight from first-principles-based calculations, and they portray a picture of a large, triangular nucleus that leads to unrealistically large depolarization and nucleation energies. Here we use atomistic molecular dynamics and coarse-grained Monte Carlo simulations to analyse these processes, and demonstrate that the prevailing models are incorrect. Our multi-scale simulations reproduce experimental domain growth rates in PbTiO3 and reveal small, square critical nuclei with a diffuse interface. A simple analytic model is also proposed, relating bulk polarization and gradient energies to wall nucleation and growth, and thus rationalizing all experimental rate measurements in PbTiO3 and BaTiO3.     

The significance of nitrification for oceanic new production

The flux of organic material sinking to depth is a major control on the inventory of carbon in the ocean. To first order, the oceanic system is at equilibrium such that what goes down must come up. Because the export flux is difficult to measure directly, it is routinely estimated indirectly by quantifying the amount of phytoplankton growth, or primary production, fuelled by the upward flux of nitrate. To do so it is necessary to take into account other sources of biologically available nitrogen. However, the generation of nitrate by nitrification in surface waters has only recently received attention. Here we perform the first synthesis of open-ocean measurements of the specific rate of surface nitrification and use these to configure a global biogeochemical model to quantify the global role of nitrification. We show that for much of the world ocean a substantial fraction of the nitrate taken up is generated through recent nitrification near the surface. At the global scale, nitrification accounts for about half of the nitrate consumed by growing phytoplankton. A consequence is that many previous attempts to quantify marine carbon export, particularly those based on inappropriate use of the f-ratio (a measure of the efficiency of the 'biological pump'), are significant overestimates.     

A second generation human haplotype map of over 3.1 million SNPs

We describe the Phase II HapMap, which characterizes over 3.1 million human single nucleotide polymorphisms (SNPs) genotyped in 270 individuals from four geographically diverse populations and includes 25-35% of common SNP variation in the populations surveyed. The map is estimated to capture untyped common variation with an average maximum r2 of between 0.9 and 0.96 depending on population. We demonstrate that the current generation of commercial genome-wide genotyping products captures common Phase II SNPs with an average maximum r2 of up to 0.8 in African and up to 0.95 in non-African populations, and that potential gains in power in association studies can be obtained through imputation. These data also reveal novel aspects of the structure of linkage disequilibrium. We show that 10-30% of pairs of individuals within a population share at least one region of extended genetic identity arising from recent ancestry and that up to 1% of all common variants are untaggable, primarily because they lie within recombination hotspots. We show that recombination rates vary systematically around genes and between genes of different function. Finally, we demonstrate increased differentiation at non-synonymous, compared to synonymous, SNPs, resulting from systematic differences in the strength or efficacy of natural selection between populations.     

Genome-wide detection and characterization of positive selection in human populations

With the advent of dense maps of human genetic variation, it is now possible to detect positive natural selection across the human genome. Here we report an analysis of over 3 million polymorphisms from the International HapMap Project Phase 2 (HapMap2). We used 'long-range haplotype' methods, which were developed to identify alleles segregating in a population that have undergone recent selection, and we also developed new methods that are based on cross-population comparisons to discover alleles that have swept to near-fixation within a population. The analysis reveals more than 300 strong candidate regions. Focusing on the strongest 22 regions, we develop a heuristic for scrutinizing these regions to identify candidate targets of selection. In a complementary analysis, we identify 26 non-synonymous, coding, single nucleotide polymorphisms showing regional evidence of positive selection. Examination of these candidates highlights three cases in which two genes in a common biological process have apparently undergone positive selection in the same population:LARGE and DMD, both related to infection by the Lassa virus, in West Africa;SLC24A5 and SLC45A2, both involved in skin pigmentation, in Europe; and EDAR and EDA2R, both involved in development of hair follicles, in Asia.     

Structural basis for synthesis of inflammatory mediators by human leukotriene C4 synthase

Cysteinyl leukotrienes are key mediators in inflammation and have an important role in acute and chronic inflammatory diseases of the cardiovascular and respiratory systems, in particular bronchial asthma. In the biosynthesis of cysteinyl leukotrienes, conversion of arachidonic acid forms the unstable epoxide leukotriene A4 (LTA4). This intermediate is conjugated with glutathione (GSH) to produce leukotriene C4 (LTC4) in a reaction catalysed by LTC4 synthase: this reaction is the key step in cysteinyl leukotriene formation. Here we present the crystal structure of the human LTC4 synthase in its apo and GSH-complexed forms to 2.00 and 2.15 A resolution, respectively. The structure reveals a homotrimer, where each monomer is composed of four transmembrane segments. The structure of the enzyme in complex with substrate reveals that the active site enforces a horseshoe-shaped conformation on GSH, and effectively positions the thiol group for activation by a nearby arginine at the membrane-enzyme interface. In addition, the structure provides a model for how the omega-end of the lipophilic co-substrate is pinned at one end of a hydrophobic cleft, providing a molecular 'ruler' to align the reactive epoxide at the thiol of glutathione. This provides new structural insights into the mechanism of LTC4 formation, and also suggests that the observed binding and activation of GSH might be common for a family of homologous proteins important for inflammatory and detoxification responses.