A formal proof of the Kepler conjecture

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project

A Stochastic Differential Equation Inventory Model

© 2018, The Author(s). Inventory for an item is being replenished at a constant rate whilst simultaneously being depleted by demand growing randomly and in relation to the inventory level. A stochastic differential equation is put forward to model this situation with solutions to it derived when analytically possible. Probabilities of reaching designated a priori inventory levels from some initial level are considered. Finally, the existence of stable inventory states is investigated by solving the Fokker–Planck equation for the diffusion process at the steady state. Investigation of the stability properties of the Fokker–Planck equation reveals that a judicious choice of control strategy allows the inventory level to remain in a stable regime

The implications of the United Nations Paris Agreement on climate change for globally significant biodiversity areas

Climate change is already affecting species and their distributions. Distributional range changes have occurred and are projected to intensify for many widespread plants and animals, creating associated risks to many ecosystems. Here, we estimate the climate change-related risks to the species in globally significant biodiversity conservation areas over a range of climate scenarios, assessing their value as climate refugia. In particular, we quantify the aggregated benefit of countries’ emission reduction pledges (Intended Nationally Determined Contributions and Nationally Determined Contributions under the Paris Agreement), and also of further constraining global warming to 2 °C above pre-industrial levels, against an unmitigated scenario of 4.5 °C warming. We also quantify the contribution that can be made by using smart spatial conservation planning to facilitate some levels of autonomous (i.e. natural) adaptation to climate change by dispersal. We find that without mitigation, on average 33% of each conservation area can act as climate refugium (or 18% if species are unable to disperse), whereas if warming is constrained to 2 °C, the average area of climate refuges doubles to 67% of each conservation area (or, without dispersal, more than doubles to 56% of each area). If the country pledges are fulfilled, an intermediate estimate of 47–52% (or 31–38%, without dispersal) is obtained. We conclude that the Nationally Determined Contributions alone have important but limited benefits for biodiversity conservation, with larger benefits accruing if warming is constrained to 2 °C. Greater benefits would result if warming was constrained to well below 2 °C as set out in the Paris Agreement

Genes Selectively Up-Regulated by Pheromone in White Cells Are Involved in Biofilm Formation in Candida albicans

To mate, MTL-homozygous strains of the yeast pathogen Candida albicans must switch from the white to opaque phase. Mating-competent opaque cells then release pheromone that induces polarization, a G1 block and conjugation tube formation in opaque cells of opposite mating type. Pheromone also induces mating-incompetent white cells to become adhesive and cohesive, and form thicker biofilms that facilitate mating. The pheromone response pathway of white cells shares the upstream components of that of opaque cells, but targets a different transcription factor. Here we demonstrate that the genes up-regulated by the pheromone in white cells are activated through a common cis-acting sequence, WPRE, which is distinct from the cis-acting sequence, OPRE, responsible for up-regulation in opaque cells. Furthermore, we find that these white-specific genes play roles in white cell biofilm formation, and are essential for biofilm formation in the absence of an added source of pheromone, suggesting either an autocrine or pheromone-independent mechanism. These results suggest an intimate, complex and unique relationship between switching, mating and MTL-homozygous white cell biofilm formation, the latter a presumed virulence factor in C. albicans

In Vivo Approaches Reveal a Key Role for DCs in CD4+ T Cell Activation and Parasite Clearance during the Acute Phase of Experimental Blood-Stage Malaria

Dendritic cells (DCs) are phagocytes that are highly specialized for antigen presentation. Heterogeneous populations of macrophages and DCs form a phagocyte network inside the red pulp (RP) of the spleen, which is a major site for the control of blood-borne infections such as malaria. However, the dynamics of splenic DCs during Plasmodium infections are poorly understood, limiting our knowledge regarding their protective role in malaria. Here, we used in vivo experimental approaches that enabled us to deplete or visualize DCs in order to clarify these issues. To elucidate the roles of DCs and marginal zone macrophages in the protection against blood-stage malaria, we infected DTx (diphtheria toxin)-treated C57BL/6.CD11c-DTR mice, as well as C57BL/6 mice treated with low doses of clodronate liposomes (ClLip), with Plasmodium chabaudi AS (Pc) parasites. The first evidence suggesting that DCs could contribute directly to parasite clearance was an early effect of the DTx treatment, but not of the ClLip treatment, in parasitemia control. DCs were also required for CD4+ T cell responses during infection. The phagocytosis of infected red blood cells (iRBCs) by splenic DCs was analyzed by confocal intravital microscopy, as well as by flow cytometry and immunofluorescence, at three distinct phases of Pc malaria: at the first encounter, at pre-crisis concomitant with parasitemia growth and at crisis when the parasitemia decline coincides with spleen closure. In vivo and ex vivo imaging of the spleen revealed that DCs actively phagocytize iRBCs and interact with CD4+ T cells both in T cell-rich areas and in the RP. Subcapsular RP DCs were highly efficient in the recognition and capture of iRBCs during pre-crisis, while complete DC maturation was only achieved during crisis. These findings indicate that, beyond their classical role in antigen presentation, DCs also contribute to the direct elimination of iRBCs during acute Plasmodium infection.São Paulo Research Foundation grants: (2011/24038-1 [MRDL], 2009/08559-1 [HBdS], CAPES/IGC 04/ 2012 [MRDL, CET])

Carotenoid Distribution in Living Cells of Haematococcus pluvialis (Chlorophyceae)

Haematococcus pluvialis is a freshwater unicellular green microalga belonging to the class Chlorophyceae and is of commercial interest for its ability to accumulate massive amounts of the red ketocarotenoid astaxanthin (3,3′-dihydroxy-β,β-carotene-4,4′-dione). Using confocal Raman microscopy and multivariate analysis, we demonstrate the ability to spectrally resolve resonance–enhanced Raman signatures associated with astaxanthin and β-carotene along with chlorophyll fluorescence. By mathematically isolating these spectral signatures, in turn, it is possible to locate these species independent of each other in living cells of H. pluvialis in various stages of the life cycle. Chlorophyll emission was found only in the chloroplast whereas astaxanthin was identified within globular and punctate regions of the cytoplasmic space. Moreover, we found evidence for β-carotene to be co-located with both the chloroplast and astaxanthin in the cytosol. These observations imply that β-carotene is a precursor for astaxanthin and the synthesis of astaxanthin occurs outside the chloroplast. Our work demonstrates the broad utility of confocal Raman microscopy to resolve spectral signatures of highly similar chromophores in living cells

Comprehensive annotation of the Parastagonospora nodorum reference genome using next-generation genomics, transcriptomics and proteogenomics

Parastagonospora nodorum, the causal agent of Septoria nodorum blotch (SNB), is an economically important pathogen of wheat (Triticum spp.), and a model for the study of necrotrophic pathology and genome evolution. The reference P. nodorum strain SN15 was the first Dothideomycete with a published genome sequence, and has been used as the basis for comparison within and between species. Here we present an updated reference genome assembly with corrections of SNP and indel errors in the underlying genome assembly from deep resequencing data as well as extensive manual annotation of gene models using transcriptomic and proteomic sources of evidence (https://github.com/robsyme/Parastagonospora_nodorum_SN15). The updated assembly and annotation includes 8,366 genes with modified protein sequence and 866 new genes. This study shows the benefits of using a wide variety of experimental methods allied to expert curation to generate a reliable set of gene models

Bacterial symbionts of the leafhopper "Evacanthus interruptus" (Linnaeus, 1758) (Insecta, Hemiptera, Cicadellidae : Evacanthinae)

Plant sap-feeding hemipterans harbor obligate symbiotic microorganisms which are responsible for the synthesis of amino acids missing in their diet. In this study, we characterized the obligate symbionts hosted in the body of the xylem-feeding leafhopper Evacanthus interruptus (Cicadellidae: Evacanthinae: Evacanthini) by means of histological, ultrastructural and molecular methods. We observed that E. interruptus is associated with two types of symbiotic microorganisms: bacterium ‘Candidatus Sulcia muelleri’ (Bacteroidetes) and betaproteobacterium that is closely related to symbionts which reside in two other Cicadellidae representatives: Pagaronia tredecimpunctata (Evacanthinae: Pagaronini) and Hylaius oregonensis (Bathysmatophorinae: Bathysmatophorini). Both symbionts are harbored in their own bacteriocytes which are localized between the body wall and ovaries. In E. interruptus, both Sulcia and betaproteobacterial symbionts are transovarially transmitted from one generation to the next. In the mature female, symbionts leave the bacteriocytes and gather around the posterior pole of the terminal oocytes. Then, they gradually pass through the cytoplasm of follicular cells surrounding the posterior pole of the oocyte and enter the space between them and the oocyte. The bacteria accumulate in the deep depression of the oolemma and form a characteristic ‘symbiont ball’. In the light of the results obtained, the phylogenetic relationships within modern Cicadomorpha and some Cicadellidae subfamilies are discussed