Families of Group Actions, Generic Isotriviality, and Linearization

We study families of reductive group actions on A2 parametrized by curves and show that every faithful action of a non-finite reductive group on A3 is linearizable, i.e. G-isomorphic to a representation of G. The difficulties arise for non-connected groups G. We prove a Generic Equivalence Theorem which says that two affine mor- phisms p: S → Y and q: T → Y of varieties with isomorphic (closed) fibers become isomorphic under a dominant ́etale base change φ : U → Y . A special case is the following result. Call a morphism φ: X → Y a fibration with fiber F if φ is flat and all fibers are (reduced and) isomorphic to F. Then an affine fibration with fiber F admits an ́etale dominant morphism μ: U → Y such that the pull-back is a trivial fiber bundle: U ×Y X ≃ U × F . As an application we give short proofs of the following two (known) results: (a) Every affine A1-fibration over a normal variety is locally trivial in the Zariski-topology; (b) Every affine A2-fibration over a smooth curve is locally trivial in the Zariski-topology

Replication in Genome-Wide Association Studies

Replication helps ensure that a genotype-phenotype association observed in a genome-wide association (GWA) study represents a credible association and is not a chance finding or an artifact due to uncontrolled biases. We discuss prerequisites for exact replication, issues of heterogeneity, advantages and disadvantages of different methods of data synthesis across multiple studies, frequentist vs. Bayesian inferences for replication, and challenges that arise from multi-team collaborations. While consistent replication can greatly improve the credibility of a genotype-phenotype association, it may not eliminate spurious associations due to biases shared by many studies. Conversely, lack of replication in well-powered follow-up studies usually invalidates the initially proposed association, although occasionally it may point to differences in linkage disequilibrium or effect modifiers across studies.Comment: Published in at http://dx.doi.org/10.1214/09-STS290 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Dynamic composition of myelin basic protein mRNA-containing ribonucleoprotein complexes

Myelin Basic Protein (MBP) is a major component of the myelin sheath orchestrating the assembly of compact myelin in the central nervous system and thus ensuring saltatory signal propagation and maintenance of the neuronal network. MBP expression is precisely regulated at the posttranscriptional level and depends on the assembly of MBP mRNA-containing granules, which mediate transport and localized translation at the axoglial contact site. This study focused on the identification of the dynamic composition of these RNP complexes and a detailed functional analysis of the previously identified potential MBP mRNA-associating proteins DDX5 and FUS. DDX5 was shown to associate with MBP mRNA in subpopulations of cytoplasmic RNP complexes. In oligodendroglial cells DDX5 functioned as an inhibitor of MBP protein synthesis, acting at the posttranscriptional level and depending on the DDX5 helicase activity. Consequently, knockdown of DDX5 in primary OL correlates with the elevation of MBP protein levels and an imbalance of the known MBP-associating RNA-binding proteins hnRNP A2 and hnRNP F. In addition, DDX5-knockdown selectively increased the expression of the exon 2-containing MBP isoforms 17.22-kDa and 21.5-kDa, possibly by affecting alternative splicing of the pre-mRNA. Alteration of FUS levels did not show a major impact on the myelin protein expression, although MBP mRNA levels were slightly reduced in line with changes in the expression of MBP mRNA-associated proteins hnRNP A2 and DDX5. During oxidative stress, FUS localized to oligodendroglial stress granules and FUS levels inversely correlated with MBP RNA stability upon increasing concentrations of sodium arsenite. To further examine the dynamic composition of MBP mRNA complexes in a more RNA-centric approach, the MS2-RNA-labeling system was adapted to MBP mRNA. The introduction of MS2 hairpin loops into the MBP transcript allowed its visualization and the purification of associated MBP mRNP complexes. Oligodendroglial cell lines stably expressing moderate levels of MS2-labeled MBP14-MS2 mRNA were generated and single molecule FISH confirmed localization and the physiological behavior of the transcript, which reacted to cellular cues such as oxidative stress. The following affinity purification of MBP14-MS2 mRNP complexes under oxidative stress conditions resulted in the identification of numerous candidates potentially playing a role in stress-dependent RNA granule formation and the regulation of MBP. This list includes several proteins connected to neurodegenerative or psychiatric diseases and may thus aid in shedding light on mechanisms regulating MBP expression during OL maturation and myelination in health and disease.138, IV Blätte

Control Function Assisted IPW Estimation with a Secondary Outcome in Case-Control Studies

Case-control studies are designed towards studying associations between risk factors and a single, primary outcome. Information about additional, secondary outcomes is also collected, but association studies targeting such secondary outcomes should account for the case-control sampling scheme, or otherwise results may be biased. Often, one uses inverse probability weighted (IPW) estimators to estimate population effects in such studies. However, these estimators are inefficient relative to estimators that make additional assumptions about the data generating mechanism. We propose a class of estimators for the effect of risk factors on a secondary outcome in case-control studies, when the mean is modeled using either the identity or the log link. The proposed estimator combines IPW with a mean zero control function that depends explicitly on a model for the primary disease outcome. The efficient estimator in our class of estimators reduces to standard IPW when the model for the primary disease outcome is unrestricted, and is more efficient than standard IPW when the model is either parametric or semiparametric

Heritability in the genome-wide association era

Heritability, the fraction of phenotypic variation explained by genetic variation, has been estimated for many phenotypes in a range of populations, organisms, and time points. The recent development of efficient genotyping and sequencing technology has led researchers to attempt to identify the genetic variants responsible for the genetic component of phenotype directly via GWAS. The gap between the phenotypic variance explained by GWAS results and those estimated from classical heritability methods has been termed the “missing heritability problem”. In this work, we examine modern methods for estimating heritability, which use the genotype and sequence data directly. We discuss them in the context of classical heritability methods, the missing heritability problem, and describe their implications for understanding the genetic architecture of complex phenotypes.National Institutes of Health (U.S.) (fellowship 5T32ES007142-27)National Institutes of Health (U.S.) (grant R21 DK084529

Exhaustive screens for disease susceptibility loci incorporating statistical interaction of genotypes: a comparison of likelihood-ratio-based and Akaike and Bayesian information criteria-based methods

Several recent papers have suggested that two-locus tests of association that incorporate gene × gene interaction can be more powerful than marginal, single-locus tests across a broad range of multilocus interaction models, even after conservative correction for multiple testing. However, because these two-locus tests are sensitive to marginal associations with either marker, they can be difficult to interpret, and it is not immediately clear how to use them to select a list of the most promising markers worthy of further study. Here we apply single- and two-locus tests to 29 single-nucleotide polymorphisms (SNPs) selected from the dense marker map in the simulated Genetic Analysis Workshop 15 data spanning several candidate regions (the HLA region, the four SNPs flanking "Locus D," and two regions on the q-arm of chromosome 6). We compare the proposed two-locus likelihood ratio tests (LRT) to Akaike and Bayesian Information Criteria (AIC and BIC) for model selection, as well as AIC- and BIC-weighted measures of "SNP importance." The latter provide summary measures of evidence for association between each SNP and disease – including potential interactions with one or more other SNPs – by summing over all one- and two-SNP models. Our results suggest that the LRT using conservative p-value criteria were sensitive (but not specific) in identifying associated markers. Standard AIC and BIC criteria were similarly sensitive but not specific. On the other hand, the AIC- and BIC-weighted importance measures yielded a specific but not very sensitive rule for SNP selection. Algorithms incorporating gene × gene interaction to prioritize markers for follow-up will require further development