On surfaces with prescribed shape operator

The problem of immersing a simply connected surface with a prescribed shape operator is discussed. I show that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space of such realizations is a convex set in an affine space of dimension at most 3. The cases where this maximum dimension of realizability is achieved are analyzed and it is found that there are two such families of shape operators, one depending essentially on three arbitrary functions of one variable and another depending essentially on two arbitrary functions of one variable. The space of realizations is discussed in each case, along with some of their remarkable geometric properties. Several explicit examples are constructed.

Distinct functions of POT1 at telomeres.

The mammalian protein POT1 binds to telomeric single-stranded DNA (ssDNA), protecting chromosome ends from being detected as sites of DNA damage. POT1 is composed of an N-terminal ssDNA-binding domain and a C-terminal protein interaction domain. With regard to the latter, POT1 heterodimerizes with the protein TPP1 to foster binding to telomeric ssDNA in vitro and binds the telomeric double-stranded-DNA-binding protein TRF2. We sought to determine which of these functions-ssDNA, TPP1, or TRF2 binding-was required to protect chromosome ends from being detected as DNA damage. Using separation-of-function POT1 mutants deficient in one of these three activities, we found that binding to TRF2 is dispensable for protecting telomeres but fosters robust loading of POT1 onto telomeric chromatin. Furthermore, we found that the telomeric ssDNA-binding activity and binding to TPP1 are required in cis for POT1 to protect telomeres. Mechanistically, binding of POT1 to telomeric ssDNA and association with TPP1 inhibit the localization of RPA, which can function as a DNA damage sensor, to telomeres.

A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses.

Antigenically variable RNA viruses are significant contributors to the burden of infectious disease worldwide. One reason for their ubiquity is their ability to escape herd immunity through rapid antigenic evolution and thereby to reinfect previously infected hosts. However, the ways in which these viruses evolve antigenically are highly diverse. Some have only limited diversity in the long-run, with every emergence of a new antigenic variant coupled with a replacement of the older variant. Other viruses rapidly accumulate antigenic diversity over time. Others still exhibit dynamics that can be considered evolutionary intermediates between these two extremes. Here, we present a theoretical framework that aims to understand these differences in evolutionary patterns by considering a virus's epidemiological dynamics in a given host population. Our framework, based on a dimensionless number, probabilistically anticipates patterns of viral antigenic diversification and thereby quantifies a virus's evolutionary potential. It is therefore similar in spirit to the basic reproduction number, the well-known dimensionless number which quantifies a pathogen's reproductive potential. We further outline how our theoretical framework can be applied to empirical viral systems, using influenza A/H3N2 as a case study. We end with predictions of our framework and work that remains to be done to further integrate viral evolutionary dynamics with disease ecology.

Desensitization, internalization, and signaling functions of beta-arrestins demonstrated by RNA interference.

Beta-arrestins bind to activated G protein-coupled receptor kinase-phosphorylated receptors, which leads to their desensitization with respect to G proteins, internalization via clathrin-coated pits, and signaling via a growing list of "scaffolded" pathways. To facilitate the discovery of novel adaptor and signaling roles of beta-arrestins, we have developed and validated a generally applicable interfering RNA approach for selectively suppressing beta-arrestins 1 or 2 expression by up to 95%. Beta-arrestin depletion in HEK293 cells leads to enhanced cAMP generation in response to beta(2)-adrenergic receptor stimulation, markedly reduced beta(2)-adrenergic receptor and angiotensin II receptor internalization and impaired activation of the MAP kinases ERK 1 and 2 by angiotensin II. This approach should allow discovery of novel signaling and regulatory roles for the beta-arrestins in many seven-membrane-spanning receptor systems.

Mix it and fix it: functions of composite olfactory signals in ring-tailed lemurs.

Animals communicating via scent often deposit composite signals that incorporate odorants from multiple sources; however, the function of mixing chemical signals remains understudied. We tested both a 'multiple-messages' and a 'fixative' hypothesis of composite olfactory signalling, which, respectively, posit that mixing scents functions to increase information content or prolong signal longevity. Our subjects-adult, male ring-tailed lemurs (Lemur catta)-have a complex scent-marking repertoire, involving volatile antebrachial (A) secretions, deposited pure or after being mixed with a squalene-rich paste exuded from brachial (B) glands. Using behavioural bioassays, we examined recipient responses to odorants collected from conspecific strangers. We concurrently presented pure A, pure B and mixed A + B secretions, in fresh or decayed conditions. Lemurs preferentially responded to mixed over pure secretions, their interest increasing and shifting over time, from sniffing and countermarking fresh mixtures, to licking and countermarking decayed mixtures. Substituting synthetic squalene (S)-a well-known fixative-for B secretions did not replicate prior results: B secretions, which contain additional chemicals that probably encode salient information, were preferred over pure S. Whereas support for the 'multiple-messages' hypothesis underscores the unique contribution from each of an animal's various secretions, support for the 'fixative' hypothesis highlights the synergistic benefits of composite signals.

Hyperpolarized Xe MR imaging of alveolar gas uptake in humans.

BACKGROUND: One of the central physiological functions of the lungs is to transfer inhaled gases from the alveoli to pulmonary capillary blood. However, current measures of alveolar gas uptake provide only global information and thus lack the sensitivity and specificity needed to account for regional variations in gas exchange. METHODS AND PRINCIPAL FINDINGS: Here we exploit the solubility, high magnetic resonance (MR) signal intensity, and large chemical shift of hyperpolarized (HP) (129)Xe to probe the regional uptake of alveolar gases by directly imaging HP (129)Xe dissolved in the gas exchange tissues and pulmonary capillary blood of human subjects. The resulting single breath-hold, three-dimensional MR images are optimized using millisecond repetition times and high flip angle radio-frequency pulses, because the dissolved HP (129)Xe magnetization is rapidly replenished by diffusive exchange with alveolar (129)Xe. The dissolved HP (129)Xe MR images display significant, directional heterogeneity, with increased signal intensity observed from the gravity-dependent portions of the lungs. CONCLUSIONS: The features observed in dissolved-phase (129)Xe MR images are consistent with gravity-dependent lung deformation, which produces increased ventilation, reduced alveolar size (i.e., higher surface-to-volume ratios), higher tissue densities, and increased perfusion in the dependent portions of the lungs. Thus, these results suggest that dissolved HP (129)Xe imaging reports on pulmonary function at a fundamental level.

Genome-wide mRNA expression correlates of viral control in CD4+ T-cells from HIV-1-infected individuals.

There is great interindividual variability in HIV-1 viral setpoint after seroconversion, some of which is known to be due to genetic differences among infected individuals. Here, our focus is on determining, genome-wide, the contribution of variable gene expression to viral control, and to relate it to genomic DNA polymorphism. RNA was extracted from purified CD4+ T-cells from 137 HIV-1 seroconverters, 16 elite controllers, and 3 healthy blood donors. Expression levels of more than 48,000 mRNA transcripts were assessed by the Human-6 v3 Expression BeadChips (Illumina). Genome-wide SNP data was generated from genomic DNA using the HumanHap550 Genotyping BeadChip (Illumina). We observed two distinct profiles with 260 genes differentially expressed depending on HIV-1 viral load. There was significant upregulation of expression of interferon stimulated genes with increasing viral load, including genes of the intrinsic antiretroviral defense. Upon successful antiretroviral treatment, the transcriptome profile of previously viremic individuals reverted to a pattern comparable to that of elite controllers and of uninfected individuals. Genome-wide evaluation of cis-acting SNPs identified genetic variants modulating expression of 190 genes. Those were compared to the genes whose expression was found associated with viral load: expression of one interferon stimulated gene, OAS1, was found to be regulated by a SNP (rs3177979, p = 4.9E-12); however, we could not detect an independent association of the SNP with viral setpoint. Thus, this study represents an attempt to integrate genome-wide SNP signals with genome-wide expression profiles in the search for biological correlates of HIV-1 control. It underscores the paradox of the association between increasing levels of viral load and greater expression of antiviral defense pathways. It also shows that elite controllers do not have a fully distinctive mRNA expression pattern in CD4+ T cells. Overall, changes in global RNA expression reflect responses to viral replication rather than a mechanism that might explain viral control.

The effect of differences in methodology among some recent applications of shearing quotients.

A shearing quotient (SQ) is a way of quantitatively representing the Phase I shearing edges on a molar tooth. Ordinary or phylogenetic least squares regression is fit to data on log molar length (independent variable) and log sum of measured shearing crests (dependent variable). The derived linear equation is used to generate an 'expected' shearing crest length from molar length of included individuals or taxa. Following conversion of all variables to real space, the expected value is subtracted from the observed value for each individual or taxon. The result is then divided by the expected value and multiplied by 100. SQs have long been the metric of choice for assessing dietary adaptations in fossil primates. Not all studies using SQ have used the same tooth position or crests, nor have all computed regression equations using the same approach. Here we focus on re-analyzing the data of one recent study to investigate the magnitude of effects of variation in 1) shearing crest inclusion, and 2) details of the regression setup. We assess the significance of these effects by the degree to which they improve or degrade the association between computed SQs and diet categories. Though altering regression parameters for SQ calculation has a visible effect on plots, numerous iterations of statistical analyses vary surprisingly little in the success of the resulting variables for assigning taxa to dietary preference. This is promising for the comparability of patterns (if not casewise values) in SQ between studies. We suggest that differences in apparent dietary fidelity of recent studies are attributable principally to tooth position examined.