Characterization of manifolds of constant curvature by spherical curves

It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the coefficients that dictate the RM frame motion (da Silva, da Silva in Mediterr J Math 15:70, 2018). Here, we shall prove the converse, i.e., we show that if all geodesic spherical curves on a Riemannian manifold are characterized by a certain linear equation, then all the geodesic spheres with a sufficiently small radius are totally umbilical and, consequently, the given manifold has constant sectional curvature. We also furnish two other characterizations in terms of (i) an inequality involving the mean curvature of a geodesic sphere and the curvature function of their curves and (ii) the vanishing of the total torsion of closed spherical curves in the case of three-dimensional manifolds. Finally, we also show that the same results are valid for semi-Riemannian manifolds of constant sectional curvature.Comment: To appear in Annali di Matematica Pura ed Applicat

A Contrast/Filling-In Model of 3-D Lightness Perception

Wallach's ratio hypothesis states that local luminance ratios clr!termine lightness perception under variable illumination. While local luminance ratios successfully discount gradual variations in illumination (illumination constancy or Type I constancy), they fail to explain lightness constancy in general. Some examples of failures of the ratio hypothesis include effects suggesting the coplanar ratio hypothesis (Gilchrist 1977), "assimilation" effects, and configural effects such as the Benary cross, and White's illusion. The present article extends the Boundary Contour System/Feature Contour System (BCS/FCS) approach to provide an explanation of these effects in terms of a neural model of 3-D lightness perception. Lightness constancy of objects in front of different backgrounds (background constancy or Type II constancy) is used to provide functional constraints to the theory and suggest a contrast negation hypothesis which states that ratio measures between coplanar regions are given more weight in the determination of lightness. Simulations of the model applied to several stimuli including Benary cross and White's illusion show that contrast negation mechanisms modulate illumination constancy mechanisms to extend the explanatory power of the model. The model is also used to devise new stimuli that test theoretical predictions

Contribution of Piezo2 to endothelium-dependent pain.

BackgroundWe evaluated the role of a mechanically-gated ion channel, Piezo2, in mechanical stimulation-induced enhancement of hyperalgesia produced by the pronociceptive vasoactive mediator endothelin-1, an innocuous mechanical stimulus-induced enhancement of hyperalgesia that is vascular endothelial cell dependent. We also evaluated its role in a preclinical model of a vascular endothelial cell dependent painful peripheral neuropathy.ResultsThe local administration of oligodeoxynucleotides antisense to Piezo2 mRNA, at the site of nociceptive testing in the rat's hind paw, but not intrathecally at the central terminal of the nociceptor, prevented innocuous stimulus-induced enhancement of hyperalgesia produced by endothelin-1 (100 ng). The mechanical hyperalgesia induced by oxaliplatin (2 mg/kg. i.v.), which was inhibited by impairing endothelial cell function, was similarly attenuated by local injection of the Piezo2 antisense. Polymerase chain reaction analysis demonstrated for the first time the presence of Piezo2 mRNA in endothelial cells.ConclusionsThese results support the hypothesis that Piezo2 is a mechano-transducer in the endothelial cell where it contributes to stimulus-dependent hyperalgesia, and a model of chemotherapy-induced painful peripheral neuropathy

Evidence for regulated expression of Telomeric Repeat-containing RNAs (TERRA) in parasitic trypanosomatids

The Telomeric Repeat-containing RNAs (TERRA) participate in the homeostasis of telomeres in higher eukaryotes. Here, we investigated the expression of TERRA in Leishmania spp. and Trypanosoma brucei and found evidences for its expression as a specific RNA class. The trypanosomatid TERRA are heterogeneous in size and partially polyadenylated. The levels of TERRA transcripts appear to be modulated through the life cycle in both trypanosomatids investigated, suggesting that TERRA play a stage-specific role in the life cycle of these early-branching eukaryotes

Functional compartmentalization of Rad9 and Hus1 reveals diverse assembly of the 9-1-1 complex components during the DNA damage response in Leishmania

The Rad9-Rad1-Hus1 (9-1-1) complex is a key component in the coordination of DNA damage sensing, cell cycle progression and DNA repair pathways in eukaryotic cells. This PCNA-related trimer is loaded onto RPA-coated single stranded DNA and interacts with ATR kinase to mediate effective checkpoint signaling to halt the cell cycle and to promote DNA repair. Beyond these core activities, mounting evidence suggests that a broader range of functions can be provided by 9-1-1 structural diversification. The protozoan parasite Leishmania is an early-branching eukaryote with a remarkably plastic genome, which hints at peculiar genome maintenance mechanisms. Here, we investigated the existence of homologs of the 9-1-1 complex subunits in L. major and found that LmRad9 and LmRad1 associate with chromatin in response to replication stress and form a complex in vivo with LmHus1. Similar to LmHus1, LmRad9 participates in telomere homeostasis and in the response to both replication stress and double strand breaks. However, LmRad9 and LmHus1-deficient cells present markedly opposite phenotypes, which suggest their functional compartmentalization. We show that some of the cellular pool of LmRad9 forms an alternative complex and that some of LmHus1 exists as a monomer. We propose that the diverse assembly of the Leishmania 9-1-1 subunits mediates functional compartmentalization, which has a direct impact on the response to genotoxic stress