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.     

Complex reorganization and predominant non-homologous repair following chromosomal breakage in karyotypically balanced germline rearrangements and transgenic integration

We defined the genetic landscape of balanced chromosomal rearrangements at nucleotide resolution by sequencing 141 breakpoints from cytogenetically interpreted translocations and inversions. We confirm that the recently described phenomenon of 'chromothripsis' (massive chromosomal shattering and reorganization) is not unique to cancer cells but also occurs in the germline, where it can resolve to a relatively balanced state with frequent inversions. We detected a high incidence of complex rearrangements (19.2%) and substantially less reliance on microhomology (31%) than previously observed in benign copy-number variants (CNVs). We compared these results to experimentally generated DNA breakage-repair by sequencing seven transgenic animals, revealing extensive rearrangement of the transgene and host genome with similar complexity to human germline alterations. Inversion was the most common rearrangement, suggesting that a combined mechanism involving template switching and non-homologous repair mediates the formation of balanced complex rearrangements that are viable, stably replicated and transmitted unaltered to subsequent generations.     

Osteoclast-poor human osteopetrosis due to mutations in the gene encoding RANKL

Autosomal recessive osteopetrosis is usually associated with normal or elevated numbers of nonfunctional osteoclasts. Here we report mutations in the gene encoding RANKL (receptor activator of nuclear factor-KB ligand) in six individuals with autosomal recessive osteopetrosis whose bone biopsy specimens lacked osteoclasts. These individuals did not show any obvious defects in immunological parameters and could not be cured by hematopoietic stem cell transplantation; however, exogenous RANKL induced formation of functional osteoclasts from their monocytes, suggesting that they could, theoretically, benefit from exogenous RANKL administration.     

Association scan of 14,500 nonsynonymous SNPs in four diseases identifies autoimmunity variants

We have genotyped 14,436 nonsynonymous SNPs (nsSNPs) and 897 major histocompatibility complex (MHC) tag SNPs from 1,000 independent cases of ankylosing spondylitis (AS), autoimmune thyroid disease (AITD), multiple sclerosis (MS) and breast cancer (BC). Comparing these data against a common control dataset derived from 1,500 randomly selected healthy British individuals, we report initial association and independent replication in a North American sample of two new loci related to ankylosing spondylitis, ARTS1 and IL23R, and confirmation of the previously reported association of AITD with TSHR and FCRL3. These findings, enabled in part by increased statistical power resulting from the expansion of the control reference group to include individuals from the other disease groups, highlight notable new possibilities for autoimmune regulation and suggest that IL23R may be a common susceptibility factor for the major 'seronegative' diseases.     

Mutations in TTBK2, encoding a kinase implicated in tau phosphorylation, segregate with spinocerebellar ataxia type 11

The microtubule-associated protein tau (encoded by MAPT) and several tau kinases have been implicated in neurodegeneration, but only MAPT has a proven role in disease. We identified mutations in the gene encoding tau tubulin kinase 2 (TTBK2) as the cause of spinocerebellar ataxia type 11. Affected brain tissue showed substantial cerebellar degeneration and tau deposition. These data suggest that TTBK2 is important in the tau cascade and in spinocerebellar degeneration.     

Optimal maintenance and replacement of extraction machinery

This paper considers a problem of optimal preventive maintenance and replacement schedule of equipment devoted to extracting resources from known deposits. Typical examples are oil drills, mine shovels, etc. At most one replacement of the existing machinery by a new one is allowed. The problem is formulated as an optimal control problem subject to the state constraint that the remaining deposit at any given time is nonnegative. We show that the optimal preventive maintenance, production rates, and the replacement and salvage times of the existing machinery and the new one, if required, can be obtained by solving sequentially a series of free-end-point optimal control problems. Moreover, an algorithm based on this result is developed and used to solve two illustrative examples.     

Crystal structure of the β2 adrenergic receptor-Gs protein complex

G protein-coupled receptors (GPCRs) are responsible for the majority of cellular responses to hormones and neurotransmitters as well as the senses of sight, olfaction and taste. The paradigm of GPCR signalling is the activation of a heterotrimeric GTP binding protein (G protein) by an agonist-occupied receptor. The β(2) adrenergic receptor (β(2)AR) activation of Gs, the stimulatory G protein for adenylyl cyclase, has long been a model system for GPCR signalling. Here we present the crystal structure of the active state ternary complex composed of agonist-occupied monomeric β(2)AR and nucleotide-free Gs heterotrimer. The principal interactions between the β(2)AR and Gs involve the amino- and carboxy-terminal α-helices of Gs, with conformational changes propagating to the nucleotide-binding pocket. The largest conformational changes in the β(2)AR include a 14 ? outward movement at the cytoplasmic end of transmembrane segment 6 (TM6) and an α-helical extension of the cytoplasmic end of TM5. The most surprising observation is a major displacement of the α-helical domain of Gαs relative to the Ras-like GTPase domain. This crystal structure represents the first high-resolution view of transmembrane signalling by a GPCR.     

ANG mutations segregate with familial and 'sporadic' amyotrophic lateral sclerosis

We recently identified angiogenin (ANG) as a candidate susceptibility gene for amyotrophic lateral sclerosis (ALS), a neurodegenerative disorder characterized by adult-onset loss of motor neurons. We now report the finding of seven missense mutations in 15 individuals, of whom four had familial ALS and 11 apparently 'sporadic' ALS. Our findings provide further evidence that variations in hypoxia-inducible genes have an important role in motor neuron degeneration.     

SLC2A9 is a newly identified urate transporter influencing serum urate concentration, urate excretion and gout

Uric acid is the end product of purine metabolism in humans and great apes, which have lost hepatic uricase activity, leading to uniquely high serum uric acid concentrations (200-500 microM) compared with other mammals (3-120 microM). About 70% of daily urate disposal occurs via the kidneys, and in 5-25% of the human population, impaired renal excretion leads to hyperuricemia. About 10% of people with hyperuricemia develop gout, an inflammatory arthritis that results from deposition of monosodium urate crystals in the joint. We have identified genetic variants within a transporter gene, SLC2A9, that explain 1.7-5.3% of the variance in serum uric acid concentrations, following a genome-wide association scan in a Croatian population sample. SLC2A9 variants were also associated with low fractional excretion of uric acid and/or gout in UK, Croatian and German population samples. SLC2A9 is a known fructose transporter, and we now show that it has strong uric acid transport activity in Xenopus laevis oocytes.