Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

Role of Δ1-Pyrroline-5-Carboxylate Dehydrogenase Supports Mitochondrial Metabolism and Host-Cell Invasion ofTrypanosoma cruzi

Proline is crucial for energizing critical events throughout the life cycle of Trypanosoma cruzi, the etiological agent of Chagas disease. The proline breakdown pathway consists of two oxidation steps, both of which producereducing equivalents as follows: the conversion of proline to Δ1-pyrroline-5-carboxylate (P5C), and the subsequent conversion of P5C to glutamate. We have identified and characterized the Δ1-pyrroline-5-carboxylate dehydrogenase from T. cruzi (TcP5CDH) and report here on how this enzyme contributes to a central metabolic pathway in this parasite. Size-exclusionchromatography, two-dimensional gel electrophoresis, and small angle x-ray scattering analysis of TcP5CDH revealed an oligomericstate composed of two subunits of six protomers. TcP5CDH was found to complement a yeast strain deficient in PUT2 activity,confirming the enzyme's functional role; and the biochemical parameters (Km, kcat, and kcat/Km) of the recombinant TcP5CDH were determined, exhibiting values comparable with those from T. cruzi lysates. In addition, TcP5CDH exhibited mitochondrial staining during the main stages of the T. cruzi life cycle. mRNA and enzymatic activity levels indicated the up-regulation (6-fold change) of TcP5CDH during the infectivestages of the parasite. The participation of P5C as an energy source was also demonstrated. Overall, we propose that thisenzymatic step is crucial for the viability of both replicative and infective forms of T. cruzi

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

Simvastatin treatment reduces the cholesterol content of membrane/lipid rafts, implicating the N -methyl-D-aspartate receptor in anxiety: a literature review

ABSTRACT Membrane/lipid rafts (MLRs) are plasmalemmal microdomains that are essential for neuronal signaling and synaptic development/stabilization. Inhibitors of 3-hydroxy-3-methylglutaryl-coenzyme-A reductase (statins) can disable the N-methyl-D-aspartate (NMDA) receptor through disruption of MLRs and, in turn, decrease NMDA-mediated anxiety. This hypothesis will contribute to understanding the critical roles of simvastatin in treating anxiety via the NMDA receptor

Phylogenomics and the rise of the angiosperms

Angiosperms are the cornerstone of most terrestrial ecosystems and human livelihoods1,2. A robust understanding of angiosperm evolution is required to explain their rise to ecological dominance. So far, the angiosperm tree of life has been determined primarily by means of analyses of the plastid genome3,4. Many studies have drawn on this foundational work, such as classification and first insights into angiosperm diversification since their Mesozoic origins5,6,7. However, the limited and biased sampling of both taxa and genomes undermines confidence in the tree and its implications. Here, we build the tree of life for almost 8,000 (about 60%) angiosperm genera using a standardized set of 353 nuclear genes8. This 15-fold increase in genus-level sampling relative to comparable nuclear studies9 provides a critical test of earlier results and brings notable change to key groups, especially in rosids, while substantiating many previously predicted relationships. Scaling this tree to time using 200 fossils, we discovered that early angiosperm evolution was characterized by high gene tree conflict and explosive diversification, giving rise to more than 80% of extant angiosperm orders. Steady diversification ensued through the remaining Mesozoic Era until rates resurged in the Cenozoic Era, concurrent with decreasing global temperatures and tightly linked with gene tree conflict. Taken together, our extensive sampling combined with advanced phylogenomic methods shows the deep history and full complexity in the evolution of a megadiverse clade