Algorithms for Colourful Simplicial Depth and Medians in the Plane

The colourful simplicial depth of a point x in the plane relative to a configuration of n points in k colour classes is exactly the number of closed simplices (triangles) with vertices from 3 different colour classes that contain x in their convex hull. We consider the problems of efficiently computing the colourful simplicial depth of a point x, and of finding a point, called a median, that maximizes colourful simplicial depth. For computing the colourful simplicial depth of x, our algorithm runs in time O(n log(n) + k n) in general, and O(kn) if the points are sorted around x. For finding the colourful median, we get a time of O(n^4). For comparison, the running times of the best known algorithm for the monochrome version of these problems are O(n log(n)) in general, improving to O(n) if the points are sorted around x for monochrome depth, and O(n^4) for finding a monochrome median.Comment: 17 pages, 8 figure

Changes in intracellular ion activities induced by adrenaline in human and rat skeletal muscle

To study the stimulating effect of adrenaline (ADR) on active Na+/K+ transport we used double-barrelled ion-sensitive micro-electrodes to measure the activities of extracellular K+ (aKe) and intracellular Na+ (aNai) in isolated preparations of rat soleus muscle, normal human intercostal muscle and one case of hyperkalemic periodic paralysis (h.p.p.). In these preparations bath-application of ADR (10−6 M) resulted in a membrane hyperpolarization and transient decreasesaKe andaNai which could be blocked by ouabain (3×10−4 M). In the h.p.p. muslce a continuous rise ofaNai induced by elevation ofaKe to 5.2 mM could be stopped by ADR. In addition, the intracellular K+ activity (aKi), the free intracellular Ca2+ concentration (pCai) and intracellular pH (pHi) were monitored in rat soleus muscle. During ADRaKi increased, pHi remained constant and intracellular Ca2+ apparently decreased. In conclusion, our data show that ADR primarily stimulates the Na+/K+ pump in mammalian skeletal muscle. This stimulating action is not impaired in the h.p.p. muscle

The mediating role of individual-level social capital among worries, mental health and subjective well-being among adults in Hong Kong during the COVID-19 pandemic

The COVID-19 pandemic has substantially induced worries and affected individual mental health and subjective well-being. Nonetheless, a high level of social capital could potentially protect individuals who suffer from mental health problems and thus promote their subjective well-being, especially under the social distancing policies during the pandemic. To this end, based on a random sample of 1053 Hong Kong adults, structural equation modeling was applied to study the path relationships between the worries of COVID-19, social capital, mental health problems, and subjective well-being. The study found that worries during the pandemic were associated with mental health and subjective well-being, through social capital as a mediator. Moreover, social capital exhibited a stronger influence on mental health and subjective well-being in the economically inactive group than in the economically active group. This study highlights the important role of social capital during the COVID-19 pandemic. While Hong Kong’s COVID-19 response has primarily focused on disease prevention, it must be noted that social services and mutual-help activities are also crucial for people to withstand the crisis

Primary cilia elongation in response to interleukin-1 mediates the inflammatory response

Primary cilia are singular, cytoskeletal organelles present in the majority of mammalian cell types where they function as coordinating centres for mechanotransduction, Wnt and hedgehog signalling. The length of the primary cilium is proposed to modulate cilia function, governed in part by the activity of intraflagellar transport (IFT). In articular cartilage, primary cilia length is increased and hedgehog signaling activated in osteoarthritis (OA). Here, we examine primary cilia length with exposure to the quintessential inflammatory cytokine interleukin-1 (IL-1), which is up-regulated in OA. We then test the hypothesis that the cilium is involved in mediating the downstream inflammatory response. Primary chondrocytes treated with IL-1 exhibited a 50 % increase in cilia length after 3 h exposure. IL-1-induced cilia elongation was also observed in human fibroblasts. In chondrocytes, this elongation occurred via a protein kinase A (PKA)-dependent mechanism. G-protein coupled adenylate cyclase also regulated the length of chondrocyte primary cilia but not downstream of IL-1. Chondrocytes treated with IL-1 exhibit a characteristic increase in the release of the inflammatory chemokines, nitric oxide and prostaglandin E2. However, in cells with a mutation in IFT88 whereby the cilia structure is lost, this response to IL-1 was significantly attenuated and, in the case of nitric oxide, completely abolished. Inhibition of IL-1-induced cilia elongation by PKA inhibition also attenuated the chemokine response. These results suggest that cilia assembly regulates the response to inflammatory cytokines. Therefore, the cilia proteome may provide a novel therapeutic target for the treatment of inflammatory pathologies, including OA

Skeletal Adaptation to Intramedullary Pressure-Induced Interstitial Fluid Flow Is Enhanced in Mice Subjected to Targeted Osteocyte Ablation

Interstitial fluid flow (IFF) is a potent regulatory signal in bone. During mechanical loading, IFF is generated through two distinct mechanisms that result in spatially distinct flow profiles: poroelastic interactions within the lacunar-canalicular system, and intramedullary pressurization. While the former generates IFF primarily within the lacunar-canalicular network, the latter generates significant flow at the endosteal surface as well as within the tissue. This gives rise to the intriguing possibility that loading-induced IFF may differentially activate osteocytes or surface-residing cells depending on the generating mechanism, and that sensation of IFF generated via intramedullary pressurization may be mediated by a non-osteocytic bone cell population. To begin to explore this possibility, we used the Dmp1-HBEGF inducible osteocyte ablation mouse model and a microfluidic system for modulating intramedullary pressure (ImP) to assess whether structural adaptation to ImP-driven IFF is altered by partial osteocyte depletion. Canalicular convective velocities during pressurization were estimated through the use of fluorescence recovery after photobleaching and computational modeling. Following osteocyte ablation, transgenic mice exhibited severe losses in bone structure and altered responses to hindlimb suspension in a compartment-specific manner. In pressure-loaded limbs, transgenic mice displayed similar or significantly enhanced structural adaptation to Imp-driven IFF, particularly in the trabecular compartment, despite up to ∼50% of trabecular lacunae being uninhabited following ablation. Interestingly, regression analysis revealed relative gains in bone structure in pressure-loaded limbs were correlated with reductions in bone structure in unpressurized control limbs, suggesting that adaptation to ImP-driven IFF was potentiated by increases in osteoclastic activity and/or reductions in osteoblastic activity incurred independently of pressure loading. Collectively, these studies indicate that structural adaptation to ImP-driven IFF can proceed unimpeded following a significant depletion in osteocytes, consistent with the potential existence of a non-osteocytic bone cell population that senses ImP-driven IFF independently and potentially parallel to osteocytic sensation of poroelasticity-derived IFF

Output from VIP cells of the mammalian central clock regulates daily physiological rhythms

The suprachiasmatic nucleus (SCN) circadian clock is critical for optimising daily cycles in mammalian physiology and behaviour. The roles of the various SCN cell types in communicating timing information to downstream physiological systems remain incompletely understood, however. In particular, while vasoactive intestinal polypeptide (VIP) signalling is essential for SCN function and whole animal circadian rhythmicity, the specific contributions of VIP cell output to physiological control remains uncertain. Here we reveal a key role for SCN VIP cells in central clock output. Using multielectrode recording and optogenetic manipulations, we show that VIP neurons provide coordinated daily waves of GABAergic input to target cells across the paraventricular hypothalamus and ventral thalamus, supressing their activity during the mid to late day. Using chemogenetic manipulation, we further demonstrate specific roles for this circuitry in the daily control of heart rate and corticosterone secretion, collectively establishing SCN VIP cells as influential regulators of physiological timing

Thoracic and Lumbar Vertebral Bone Mineral Density Changes in a Natural Occurring Dog Model of Diffuse Idiopathic Skeletal Hyperostosis

Ankylosing spinal disorders can be associated with alterations in vertebral bone mineral density (BMD). There is however controversy about vertebral BMD in patients wuse idiopathic skeletal hyperostosis (DISH). DISH in Boxer dogs has been considered a natural occurring disease model for DISH in people. The purpose of this study was to compare vertebral BMD between Boxers with and without DISH. Fifty-nine Boxers with (n=30) or without (n=29) DISH that underwent computed tomography were included. Vertebral BMD was calculated for each thoracic and lumbar vertebra by using an earlier reported and validated protocol. For each vertebral body, a region of interest was drawn on the axial computed tomographic images at three separate locations: immediately inferior to the superior end plate, in the middle of the vertebral body, and superior to the inferior end plate. Values from the three axial slices were averaged to give a mean Hounsfield Unit value for each vertebral body. Univariate statistical analysis was performed to identify factors to be included in a multivariate model. The multivariate model including all dogs demonstrated that vertebral DISH status (Coefficient 24.63; 95% CI 16.07 to 33.19; p <0.001), lumbar vertebrae (Coefficient -17.25; 95% CI -23.42 to -11.09; p < 0.01), and to a lesser extent higher age (Coefficient -0.56; 95% CI -1.07 to -0.05; p = 0.03) were significant predictors for vertebral BMD. When the multivariate model was repeated using only dogs with DISH, vertebral DISH status (Coefficient 20.67; 95% CI, 10.98 to 30.37; p < 0.001) and lumbar anatomical region (Coefficient -38.24; 95% CI, -47.75 to -28.73; p < 0.001) were again predictors for vertebral BMD but age was not. The results of this study indicate that DISH can be associated with decreased vertebral BMD. Further studies are necessary to evaluate the clinical importance and pathophysiology of this finding