A spinor approach to Walker geometry

A four-dimensional Walker geometry is a four-dimensional manifold M with a neutral metric g and a parallel distribution of totally null two-planes. This distribution has a natural characterization as a projective spinor field subject to a certain constraint. Spinors therefore provide a natural tool for studying Walker geometry, which we exploit to draw together several themes in recent explicit studies of Walker geometry and in other work of Dunajski (2002) and Plebanski (1975) in which Walker geometry is implicit. In addition to studying local Walker geometry, we address a global question raised by the use of spinors.Comment: 41 pages. Typos which persisted into published version corrected, notably at (2.15

A single zinc finger optimizes the DNA interactions of the nucleocapsid protein of the yeast retrotransposon Ty3

Reverse transcription in retroviruses and retrotransposons requires nucleic acid chaperones, which drive the rearrangement of nucleic acid conformation. The nucleic acid chaperone properties of the human immunodeficiency virus type-1 (HIV-1) nucleocapsid (NC) protein have been extensively studied, and nucleic acid aggregation, duplex destabilization and rapid binding kinetics have been identified as major components of its activity. However, the properties of other nucleic acid chaperone proteins, such as retrotransposon Ty3 NC, a likely ancestor of HIV-1 NC, are not well understood. In addition, it is unclear whether a single zinc finger is sufficient to optimize the properties characteristic of HIV-1 NC. We used single-molecule DNA stretching as a method for detailed characterization of Ty3 NC chaperone activity. We found that wild type Ty3 NC aggregates single- and double-stranded DNA, weakly stabilizes dsDNA, and exhibits rapid binding kinetics. Single-molecule studies in the presence of Ty3 NC mutants show that the N-terminal basic residues and the unique zinc finger at the C-terminus are required for optimum chaperone activity in this system. While the single zinc finger is capable of optimizing Ty3 NC's DNA interaction kinetics, two zinc fingers may be necessary in order to facilitate the DNA destabilization exhibited by HIV-1 NC

Lagrange-Fedosov Nonholonomic Manifolds

We outline an unified approach to geometrization of Lagrange mechanics, Finsler geometry and geometric methods of constructing exact solutions with generic off-diagonal terms and nonholonomic variables in gravity theories. Such geometries with induced almost symplectic structure are modelled on nonholonomic manifolds provided with nonintegrable distributions defining nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and Fedosov nonholonomic manifolds provided with almost symplectic connection adapted to the nonlinear connection structure. We investigate the main properties of generalized Fedosov nonholonomic manifolds and analyze exact solutions defining almost symplectic Einstein spaces.Comment: latex2e, v3, published variant, with new S.V. affiliatio

A single amino acid substitution in ORF1 dramatically decreases L1 retrotransposition and provides insight into nucleic acid chaperone activity

L1 is a ubiquitous interspersed repeated sequence in mammals that achieved its high copy number by autonomous retrotransposition. Individual L1 elements within a genome differ in sequence and retrotransposition activity. Retrotransposition requires two L1-encoded proteins, ORF1p and ORF2p. Chimeric elements were used to map a 15-fold difference in retrotransposition efficiency between two L1 variants from the mouse genome, TFC and TFspa, to a single amino acid substitution in ORF1p, D159H. The steady-state levels of L1 RNA and protein do not differ significantly between these two elements, yet new insertions are detected earlier and at higher frequency in TFC, indicating that it converts expressed L1 intermediates more effectively into new insertions. The two ORF1 proteins were purified and their nucleic acid binding and chaperone activities were examined in vitro. Although the RNA and DNA oligonucleotide binding affinities of these two ORF1 proteins were largely indistinguishable, D159 was significantly more effective as a nucleic acid chaperone than H159. These findings support a requirement for ORF1p nucleic acid chaperone activity at a late step during L1 retrotransposition, extend the region of ORF1p that is known to be critical for its functional interactions with nucleic acids, and enhance understanding of nucleic acid chaperone activity

Novel integrative genomic tool for interrogating lithium response in bipolar disorder

We developed a novel integrative genomic tool called GRANITE (Genetic Regulatory Analysis of Networks Investigational Tool Environment) that can effectively analyze large complex data sets to generate interactive networks. GRANITE is an open-source tool and invaluable resource for a variety of genomic fields. Although our analysis is confined to static expression data, GRANITE has the capability of evaluating time-course data and generating interactive networks that may shed light on acute versus chronic treatment, as well as evaluating dose response and providing insight into mechanisms that underlie therapeutic versus sub-therapeutic doses or toxic doses. As a proof-of-concept study, we investigated lithium (Li) response in bipolar disorder (BD). BD is a severe mood disorder marked by cycles of mania and depression. Li is one of the most commonly prescribed and decidedly effective treatments for many patients (responders), although its mode of action is not yet fully understood, nor is it effective in every patient (non-responders). In an in vitro study, we compared vehicle versus chronic Li treatment in patient-derived lymphoblastoid cells (LCLs) (derived from either responders or non-responders) using both microRNA (miRNA) and messenger RNA gene expression profiling. We present both Li responder and non-responder network visualizations created by our GRANITE analysis in BD. We identified by network visualization that the Let-7 family is consistently downregulated by Li in both groups where this miRNA family has been implicated in neurodegeneration, cell survival and synaptic development. We discuss the potential of this analysis for investigating treatment response and even providing clinicians with a tool for predicting treatment response in their patients, as well as for providing the industry with a tool for identifying network nodes as targets for novel drug discovery

On paraquaternionic submersions between paraquaternionic K\"ahler manifolds

In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic K\"ahler non locally hyper paraK\"ahler manifolds. Then we examine, as an example, the canonical projection of the tangent bundle, endowed with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.Comment: 13 pages, no figure

Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem for the natural diagonal (almost) para-K\"ahlerian structures on the total spaces of the cotangent bundle.Comment: 10 pages, will appear in Czechoslovak Mathematical Journa

Reliability of a novel approach for reference-based cell type estimation in human placental DNA methylation studies

The placenta is a central organ during early development, influencing trajectories of health and disease. DNA methylation (DNAm) studies of human placenta improve our understanding of how its function relates to disease risk. However, DNAm studies can be biased by cell type heterogeneity, so it is essential to control for this in order to reduce confounding and increase precision. Computational cell type deconvolution approaches have proven to be very useful for this purpose. For human placenta, however, an assessment of the performance of these estimation methods is still lacking. Here, we examine the performance of a newly available reference-based cell type estimation approach and compare it to an often-used reference-free cell type estimation approach, namely RefFreeEWAS, in placental genome-wide DNAm samples taken at birth and from chorionic villus biopsies early in pregnancy using three independent studies comprising over 1000 samples. We found both reference-free and reference-based estimated cell type proportions to have predictive value for DNAm, however, reference-based cell type estimation outperformed reference-free estimation for the majority of data sets. Reference-based cell type estimations mirror previous histological knowledge on changes in cell type proportions through gestation. Further, CpGs whose variation in DNAm was largely explained by reference-based estimated cell type proportions were in the proximity of genes that are highly tissue-specific for placenta. This was not the case for reference-free estimated cell type proportions. We provide a list of these CpGs as a resource to help researchers to interpret results of existing studies and improve future DNAm studies of human placenta.Peer reviewe