Maximum coverage with cluster constraints: An LP-based approximation technique

Packing problems constitute an important class of optimization problems. However, despite the large number of variants that have been studied in the literature, most packing problems encompass a single tier of capacity restrictions only. For example, in the Multiple Knapsack Problem, we want to assign a selection of items to multiple knapsacks such that their capacities are not exceeded. But what if these knapsacks are partitioned into clusters, each imposing an additional (aggregated) capacity restriction on the knapsacks contained in that cluster? In this paper, we study the Maximum Coverage Problem with Cluster Constraints (MCPC), which generalizes the Maximum Coverage Problem with Knapsack Constraints (MCPK) by incorporating such cluster constraints. Our main contribution is a general LP-based technique to derive approximation algorithms for such cluster capacitated problems. Our technique basically allows us to reduce the cluster capacitated problem to the respective original packing problem. By using an LP-based approximation algorithm for the original problem, we can then obtain an effective rounding scheme for the problem, which only loses a small fraction in the approximation guarantee. We apply our technique to derive approximation algorithms for MCPC. To this aim, we develop an LP-based 12(1−1e) -approximation algorithm for MCPK by adapting the pipage rounding technique. Combined with our reduction technique, we obtain a 13(1−1e) -approximation algorithm for MCPC. We also derive improved results for a special case of MCPC, the Multiple Knapsack Problem with Cluster Constraints (MKPC). Based on a simple greedy algorithm, our approach yields a 13 -approximation algorithm. By combining our technique with a more sophisticated iterative rounding approach, we obtain a 12 -approximation algorithm for certain special cases of MKPC

Definition of the σW regulon of Bacillus subtilis in the absence of stress

Bacteria employ extracytoplasmic function (ECF) sigma factors for their responses to environmental stresses. Despite intensive research, the molecular dissection of ECF sigma factor regulons has remained a major challenge due to overlaps in the ECF sigma factor-regulated genes and the stimuli that activate the different ECF sigma factors. Here we have employed tiling arrays to single out the ECF σW regulon of the Gram-positive bacterium Bacillus subtilis from the overlapping ECF σX, σY, and σM regulons. For this purpose, we profiled the transcriptome of a B. subtilis sigW mutant under non-stress conditions to select candidate genes that are strictly σW-regulated. Under these conditions, σW exhibits a basal level of activity. Subsequently, we verified the σW-dependency of candidate genes by comparing their transcript profiles to transcriptome data obtained with the parental B. subtilis strain 168 grown under 104 different conditions, including relevant stress conditions, such as salt shock. In addition, we investigated the transcriptomes of rasP or prsW mutant strains that lack the proteases involved in the degradation of the σW anti-sigma factor RsiW and subsequent activation of the σW-regulon. Taken together, our studies identify 89 genes as being strictly σW-regulated, including several genes for non-coding RNAs. The effects of rasP or prsW mutations on the expression of σW-dependent genes were relatively mild, which implies that σW-dependent transcription under non-stress conditions is not strictly related to RasP and PrsW. Lastly, we show that the pleiotropic phenotype of rasP mutant cells, which have defects in competence development, protein secretion and membrane protein production, is not mirrored in the transcript profile of these cells. This implies that RasP is not only important for transcriptional regulation via σW, but that this membrane protease also exerts other important post-transcriptional regulatory functions

Prolonged fibroblast growth factor 19 response in patients with primary sclerosing cholangitis after an oral chenodeoxycholic acid challenge

Bile salts likely contribute to liver injury in patients with primary sclerosing cholangitis (PSC) and primary biliary cholangitis (PBC). Fibroblast growth factor 19 (FGF19) is a bile salt-induced enterokine with hepatoprotective potential as it suppresses de novo bile salt synthesis. Here, we evaluated the bile salt receptor FXR/FGF19 gut-liver axis in PSC and PBC patients. Fasted patients with PSC (n = 12) and PBC (n = 10), and healthy controls (HC; n = 10) were orally challenged with the natural FXR agonist chenodeoxycholic acid (CDCA 15 mg/kg). Blood was sampled hourly until 8 h afterwards. Serum FGF19 and bile salt excursions were determined. Serum levels of 7 alpha-hydroxy-4-cholesten-3-one (C4), reflecting bile salt synthesis, were measured as a biomarker of FGF19 response. Baseline serum FGF19 levels were comparable between groups, while fasted bile salt levels in PSC patients were elevated. Upon CDCA challenge, HC and PBC patients showed a serum FGF19 peak after 4 h followed by a decline. PSC patients showed a prolonged and elevated serum FGF19 response up to 8 h, combined with a sustained serum elevation of CDCA and other bile salts. In general, C4 levels declined following FGF19 elevation. In PSC patients with less favorable prognosis, baseline C4 levels were drastically suppressed and did not further decline. Following an oral CDCA challenge, PSC patients showed an impaired clearance of CDCA and a prolonged serum FGF19 response. FXR agonist therapy in PSC could cause prolonged exposure to elevated levels of FGF19, and we propose careful monitoring for detrimental side effects in patient studies

Oral ribose supplementation in dystroglycanopathy:A single case study

Three forms of muscular dystrophy-dystroglycanopathies are linked to the ribitol pathway. These include mutations in the isoprenoid synthase domain-containing protein (ISPD), fukutin-related protein (FKRP), and fukutin (FKTN) genes. The aforementioned enzymes are required for generation of the ribitol phosphate linkage in the O-glycan of alpha-dystroglycan. Mild cases of dystroglycanopathy present with slowly progressive muscle weakness, while in severe cases the eyes and brain are also involved. Previous research showed that ribose increased the intracellular concentrations of cytidine diphosphate-ribitol (CDP-ribitol) and had a therapeutic effect. Here, we report the safety and effects of oral ribose supplementation during 6 months in a patient with limb girdle muscular dystrophy type 2I (LGMD2I) due to a homozygous FKRP mutation. Ribose was well tolerated in doses of 9 g or 18 g/day. Supplementation with 18 g of ribose resulted in a decrease of creatine kinase levels of 70%. Moreover, metabolomics showed a significant increase in CDP-ribitol levels with 18 g of ribose supplementation (p &lt; 0.001). Although objective improvement in clinical and patient-reported outcome measures was not observed, the patient reported subjective improvement of muscle strength, fatigue, and pain. This case study indicates that ribose supplementation in patients with dystroglycanopathy is safe and highlights the importance for future studies regarding its potential effects.</p

Analysis of obstetric complications and uterine connective tissue in tenascin-X-deficient humans and mice

Tenascin-X (TNX) is a large, multi-domain, extracellular matrix glycoprotein. Complete deficiency of TNX in humans leads to a recessive form of Ehlers-Danlos syndrome (EDS), and TNX haploinsufficiency is a cause of hypermobility type EDS. EDS patients appear to have a higher risk of several complications during pregnancy, such as pelvic instability, premature rupture of membranes, and postpartum hemorrhage. Here, we present a study of genitourinary and obstetric complications in TNX-deficient women of reproductive age. We have found complications, such as uterus prolapses, that are in agreement with previous findings in other EDS types. In TNX knockout (KO) mice, we have observed mild pregnancy-related abnormalities. Morphological and immunohistological analysis of uterine tissues has not revealed obvious quantitative or spatial differences between TNX KO and wildtype mice with respect to collagen types I, III, V, and XII or elastic fibers. We conclude that TNX-deficient women are at risk of obstetric complications, but that TNX KO mice show only a mild phenotype. Furthermore, we show that TNX is involved in the stability of elastic fibers rather than in their initial deposition

Molecular and cellular mechanisms underlying the evolution of form and function in the amniote jaw.

The amniote jaw complex is a remarkable amalgamation of derivatives from distinct embryonic cell lineages. During development, the cells in these lineages experience concerted movements, migrations, and signaling interactions that take them from their initial origins to their final destinations and imbue their derivatives with aspects of form including their axial orientation, anatomical identity, size, and shape. Perturbations along the way can produce defects and disease, but also generate the variation necessary for jaw evolution and adaptation. We focus on molecular and cellular mechanisms that regulate form in the amniote jaw complex, and that enable structural and functional integration. Special emphasis is placed on the role of cranial neural crest mesenchyme (NCM) during the species-specific patterning of bone, cartilage, tendon, muscle, and other jaw tissues. We also address the effects of biomechanical forces during jaw development and discuss ways in which certain molecular and cellular responses add adaptive and evolutionary plasticity to jaw morphology. Overall, we highlight how variation in molecular and cellular programs can promote the phenomenal diversity and functional morphology achieved during amniote jaw evolution or lead to the range of jaw defects and disease that affect the human condition

Flexibility along the Neck of the Neogene Terror Bird Andalgalornis steulleti (Aves Phorusrhacidae)

BACKGROUND: Andalgalornis steulleti from the upper Miocene-lower Pliocene (≈6 million years ago) of Argentina is a medium-sized patagornithine phorusrhacid. It was a member of the predominantly South American radiation of 'terror birds' (Phorusrhacidae) that were apex predators throughout much of the Cenozoic. A previous biomechanical study suggests that the skull would be prepared to make sudden movements in the sagittal plane to subdue prey. METHODOLOGY/PRINCIPAL FINDINGS: We analyze the flexion patterns of the neck of Andalgalornis based on the neck vertebrae morphology and biometrics. The transitional cervical vertebrae 5th and 9th clearly separate regions 1-2 and 2-3 respectively. Bifurcate neural spines are developed in the cervical vertebrae 7th to 12th suggesting the presence of a very intricate ligamentary system and of a very well developed epaxial musculature. The presence of the lig. elasticum interespinale is inferred. High neural spines of R3 suggest that this region concentrates the major stresses during downstrokes. CONCLUSIONS/SIGNIFICANCE: The musculoskeletal system of Andalgalornis seems to be prepared (1) to support a particularly big head during normal stance, and (2) to help the neck (and the head) rising after the maximum ventroflexion during a strike. The study herein is the first interpretation of the potential performance of the neck of Andalgalornis in its entirety and we considered this an important starting point to understand and reconstruct the flexion pattern of other phorusrhacids from which the neck is unknown