On Spacetimes with Constant Scalar Invariants

We study Lorentzian spacetimes for which all scalar invariants constructed from the Riemann tensor and its covariant derivatives are constant ($CSI$ spacetimes). We obtain a number of general results in arbitrary dimensions. We study and construct warped product $CSI$ spacetimes and higher-dimensional Kundt $CSI$ spacetimes. We show how these spacetimes can be constructed from locally homogeneous spaces and $VSI$ spacetimes. The results suggest a number of conjectures. In particular, it is plausible that for $CSI$ spacetimes that are not locally homogeneous the Weyl type is $II$, $III$, $N$ or $O$, with any boost weight zero components being constant. We then consider the four-dimensional $CSI$ spacetimes in more detail. We show that there are severe constraints on these spacetimes, and we argue that it is plausible that they are either locally homogeneous or that the spacetime necessarily belongs to the Kundt class of $CSI$ spacetimes, all of which are constructed. The four-dimensional results lend support to the conjectures in higher dimensions.Comment: 25 pages, 1 figure, v2: minor changes throughou

EphA2/Ephrin-A1 Mediate Corneal Epithelial Cell Compartmentalization via ADAM10 Regulation of EGFR Signaling.

Purpose: Progenitor cells of the limbal epithelium reside in a discrete area peripheral to the more differentiated corneal epithelium and maintain tissue homeostasis. What regulates the limbal-corneal epithelial boundary is a major unanswered question. Ephrin-A1 ligand is enriched in the limbal epithelium, whereas EphA2 receptor is concentrated in the corneal epithelium. This reciprocal pattern led us to assess the role of ephrin-A1 and EphA2 in limbal-corneal epithelial boundary organization. Methods: EphA2-expressing corneal epithelial cells engineered to express ephrin-A1 were used to study boundary formation in vitro in a manner that mimicked the relative abundance of these juxtamembrane signaling proteins in the limbal and corneal epithelium in vivo. Interaction of these two distinct cell populations following initial seeding into discrete culture compartments was assessed by live cell imaging. Immunofluoresence and immunoblotting was used to evaluate the contribution of downstream growth factor signaling and cell-cell adhesion systems to boundary formation at sites of heterotypic contact between ephrin-A1 and EphA2 expressing cells. Results: Ephrin-A1-expressing cells impeded and reversed the migration of EphA2-expressing corneal epithelial cells upon heterotypic contact formation leading to coordinated migration of the two cell populations in the direction of an ephrin-A1-expressing leading front. Genetic silencing and pharmacologic inhibitor studies demonstrated that the ability of ephrin-A1 to direct migration of EphA2-expressing cells depended on an a disintegrin and metalloproteinase domain-containing protein 10 (ADAM10) and epidermal growth factor receptor (EGFR) signaling pathway that limited E-cadherin-mediated adhesion at heterotypic boundaries. Conclusions: Ephrin-A1/EphA2 signaling complexes play a key role in limbal-corneal epithelial compartmentalization and the response of these tissues to injury

Local and global modes of drug action in biochemical networks

It becomes increasingly accepted that a shift is needed from the traditional target-based approach of drug development to an integrated perspective of drug action in biochemical systems. We here present an integrative analysis of the interactions between drugs and metabolism based on the concept of drug scope. The drug scope represents the set of metabolic compounds and reactions that are potentially affected by a drug. We constructed and analyzed the scopes of all US approved drugs having metabolic targets. Our analysis shows that the distribution of drug scopes is highly uneven, and that drugs can be classified into several categories based on their scopes. Some of them have small scopes corresponding to localized action, while others have large scopes corresponding to potential large-scale systemic action. These groups are well conserved throughout different topologies of the underlying metabolic network. They can furthermore be associated to specific drug therapeutic properties

Opposing brain differences in 16p11.2 deletion and duplication carriers

Deletions and duplications of the recurrent ∼600 kb chromosomal BP4–BP5 region of 16p11.2 are associated with a broad variety of neurodevelopmental outcomes including autism spectrum disorder. A clue to the pathogenesis of the copy number variant (CNV)'s effect on the brain is that the deletion is associated with a head size increase, whereas the duplication is associated with a decrease. Here we analyzed brain structure in a clinically ascertained group of human deletion (N = 25) and duplication (N = 17) carriers from the Simons Variation in Individuals Project compared with age-matched controls (N = 29 and 33, respectively). Multiple brain measures showed increased size in deletion carriers and reduced size in duplication carriers. The effects spanned global measures of intracranial volume, brain size, compartmental measures of gray matter and white matter, subcortical structures, and the cerebellum. Quantitatively, the largest effect was on the thalamus, but the collective results suggest a pervasive rather than a selective effect on the brain. Detailed analysis of cortical gray matter revealed that cortical surface area displays a strong dose-dependent effect of CNV (deletion > control > duplication), whereas average cortical thickness is less affected. These results suggest that the CNV may exert its opposing influences through mechanisms that influence early stages of embryonic brain development

Gene Function Classification Using Bayesian Models with Hierarchy-Based Priors

We investigate the application of hierarchical classification schemes to the annotation of gene function based on several characteristics of protein sequences including phylogenic descriptors, sequence based attributes, and predicted secondary structure. We discuss three Bayesian models and compare their performance in terms of predictive accuracy. These models are the ordinary multinomial logit (MNL) model, a hierarchical model based on a set of nested MNL models, and a MNL model with a prior that introduces correlations between the parameters for classes that are nearby in the hierarchy. We also provide a new scheme for combining different sources of information. We use these models to predict the functional class of Open Reading Frames (ORFs) from the E. coli genome. The results from all three models show substantial improvement over previous methods, which were based on the C5 algorithm. The MNL model using a prior based on the hierarchy outperforms both the non-hierarchical MNL model and the nested MNL model. In contrast to previous attempts at combining these sources of information, our approach results in a higher accuracy rate when compared to models that use each data source alone. Together, these results show that gene function can be predicted with higher accuracy than previously achieved, using Bayesian models that incorporate suitable prior information

Locked Nucleic Acid Pentamers as Universal PCR Primers for Genomic DNA Amplification

Background: Multiplexing technologies, which allow for simultaneous detection of multiple nucleic acid sequences in a single reaction, can save a lot of time, cost and labor compared to traditional single reaction detection methods. However, the multiplexing method currently used requires precise handiwork and many complicated steps, making a new, simpler technique desirable. Oligonucleotides containing locked nucleic acid residues are an attractive tool because they have strong affinities for their complementary targets, they have been used to avoid dimer formation and mismatch hybridization and to enhance efficient priming. In this study, we aimed to investigate the use of locked nucleic acid pentamers for genomic DNA amplification and multiplex genotyping. Results: We designed locked nucleic acid pentamers as universal PCR primers for genomic DNA amplification. The locked nucleic acid pentamers were able to prime amplification of the selected sequences within the investigated genomes, and the resulting products were similar in length to those obtained by restriction digest. In Real Time PCR of genomic DNA from three bacterial species, locked nucleic acid pentamers showed high priming efficiencies. Data from bias tests demonstrated that locked nucleic acid pentamers have equal affinities for each of the six genes tested from the Klebsiella pneumoniae genome. Combined with suspension array genotyping, locked nucleic acid pentamer-based PCR amplification was able to identify a total of 15 strains, including 3 species of bacteria, by gene- and species-specific probes. Among the 32 specie

How Well Do We (and Will We) Know Solar Neutrino Fluxes and Oscillation Parameters?

Assuming neutrino oscillations occur, the pp electron neutrino flux is uncertain by at least a factor of two, the ${\rm ^8B}$ flux by a factor of five, and the ${\rm ^7Be}$ flux by a factor of forty-five. Calculations of the expected results of future solar neutrino experiments (SuperKamiokande, SNO, BOREXINO, ICARUS, HELLAZ, and HERON) are used to illustrate the extent to which these experiments will restrict the range of the allowed neutrino mixing parameters. We present an improved formulation of the ``luminosity constraint'' and show that at 95\% confidence limit this constraint establishes the best available limits on the rate of creation of pp neutrinos in the solar interior and provides the best upper limit to the ${\rm ^7Be}$ neutrino flux.Comment: 37 pages, uuencoded Z-compressed postscript file (with figures); Submitted to Physical Review

Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area