Asymptotic Spectral Measures, Quantum Mechanics, and E-theory

We study the relationship between POV-measures in quantum theory and asymptotic morphisms in the operator algebra E-theory of Connes-Higson. This is done by introducing the theory of "asymptotic" PV-measures and their integral correspondence with positive asymptotic morphisms on locally compact spaces. Examples and applications involving various aspects of quantum physics, including quantum noise models, semiclassical limits, strong deformation quantizations, and pure half-spin particles, are also discussed.Comment: For journal version, see http://link.springer.de/link/service/journals/00220/bibs/2226001/22260041.ht

An atlas of dynamic chromatin landscapes in mouse fetal development

The Encyclopedia of DNA Elements (ENCODE) project has established a genomic resource for mammalian development, profiling a diverse panel of mouse tissues at 8 developmental stages from 10.5 days after conception until birth, including transcriptomes, methylomes and chromatin states. Here we systematically examined the state and accessibility of chromatin in the developing mouse fetus. In total we performed 1,128 chromatin immunoprecipitation with sequencing (ChIP–seq) assays for histone modifications and 132 assay for transposase-accessible chromatin using sequencing (ATAC–seq) assays for chromatin accessibility across 72 distinct tissue-stages. We used integrative analysis to develop a unified set of chromatin state annotations, infer the identities of dynamic enhancers and key transcriptional regulators, and characterize the relationship between chromatin state and accessibility during developmental gene regulation. We also leveraged these data to link enhancers to putative target genes and demonstrate tissue-specific enrichments of sequence variants associated with disease in humans. The mouse ENCODE data sets provide a compendium of resources for biomedical researchers and achieve, to our knowledge, the most comprehensive view of chromatin dynamics during mammalian fetal development to date

Multigenome DNA sequence conservation identifies Hox cis-regulatory elements

To learn how well ungapped sequence comparisons of multiple species can predict cis-regulatory elements in Caenorhabditis elegans, we made such predictions across the large, complex ceh-13/lin-39 locus and tested them transgenically. We also examined how prediction quality varied with different genomes and parameters in our comparisons. Specifically, we sequenced ∼0.5% of the C. brenneri and C. sp. 3 PS1010 genomes, and compared five Caenorhabditis genomes (C. elegans, C. briggsae, C. brenneri, C. remanei, and C. sp. 3 PS1010) to find regulatory elements in 22.8 kb of noncoding sequence from the ceh-13/lin-39 Hox subcluster. We developed the MUSSA program to find ungapped DNA sequences with N-way transitive conservation, applied it to the ceh-13/lin-39 locus, and transgenically assayed 21 regions with both high and low degrees of conservation. This identified 10 functional regulatory elements whose activities matched known ceh-13/lin-39 expression, with 100% specificity and a 77% recovery rate. One element was so well conserved that a similar mouse Hox cluster sequence recapitulated the native nematode expression pattern when tested in worms. Our findings suggest that ungapped sequence comparisons can predict regulatory elements genome-wide

Mining gene expression data by interpreting principal components

BACKGROUND: There are many methods for analyzing microarray data that group together genes having similar patterns of expression over all conditions tested. However, in many instances the biologically important goal is to identify relatively small sets of genes that share coherent expression across only some conditions, rather than all or most conditions as required in traditional clustering; e.g. genes that are highly up-regulated and/or down-regulated similarly across only a subset of conditions. Equally important is the need to learn which conditions are the decisive ones in forming such gene sets of interest, and how they relate to diverse conditional covariates, such as disease diagnosis or prognosis. RESULTS: We present a method for automatically identifying such candidate sets of biologically relevant genes using a combination of principal components analysis and information theoretic metrics. To enable easy use of our methods, we have developed a data analysis package that facilitates visualization and subsequent data mining of the independent sources of significant variation present in gene microarray expression datasets (or in any other similarly structured high-dimensional dataset). We applied these tools to two public datasets, and highlight sets of genes most affected by specific subsets of conditions (e.g. tissues, treatments, samples, etc.). Statistically significant associations for highlighted gene sets were shown via global analysis for Gene Ontology term enrichment. Together with covariate associations, the tool provides a basis for building testable hypotheses about the biological or experimental causes of observed variation. CONCLUSION: We provide an unsupervised data mining technique for diverse microarray expression datasets that is distinct from major methods now in routine use. In test uses, this method, based on publicly available gene annotations, appears to identify numerous sets of biologically relevant genes. It has proven especially valuable in instances where there are many diverse conditions (10's to hundreds of different tissues or cell types), a situation in which many clustering and ordering algorithms become problematic. This approach also shows promise in other topic domains such as multi-spectral imaging datasets

A mathematical and computational framework for quantitative comparison and integration of large-scale gene expression data

Analysis of large-scale gene expression studies usually begins with gene clustering. A ubiquitous problem is that different algorithms applied to the same data inevitably give different results, and the differences are often substantial, involving a quarter or more of the genes analyzed. This raises a series of important but nettlesome questions: How are different clustering results related to each other and to the underlying data structure? Is one clustering objectively superior to another? Which differences, if any, are likely candidates to be biologically important? A systematic and quantitative way to address these questions is needed, together with an effective way to integrate and leverage expression results with other kinds of large-scale data and annotations. We developed a mathematical and computational framework to help quantify, compare, visualize and interactively mine clusterings. We show that by coupling confusion matrices with appropriate metrics (linear assignment and normalized mutual information scores), one can quantify and map differences between clusterings. A version of receiver operator characteristic analysis proved effective for quantifying and visualizing cluster quality and overlap. These methods, plus a flexible library of clustering algorithms, can be called from a new expandable set of software tools called CompClust 1.0 (). CompClust also makes it possible to relate expression clustering patterns to DNA sequence motif occurrences, protein–DNA interaction measurements and various kinds of functional annotations. Test analyses used yeast cell cycle data and revealed data structure not obvious under all algorithms. These results were then integrated with transcription motif and global protein–DNA interaction data to identify G(1) regulatory modules

An atlas of dynamic chromatin landscapes in mouse fetal development

The Encyclopedia of DNA Elements (ENCODE) project has established a genomic resource for mammalian development, profiling a diverse panel of mouse tissues at 8 developmental stages from 10.5 days after conception until birth, including transcriptomes, methylomes and chromatin states. Here we systematically examined the state and accessibility of chromatin in the developing mouse fetus. In total we performed 1,128 chromatin immunoprecipitation with sequencing (ChIP–seq) assays for histone modifications and 132 assay for transposase-accessible chromatin using sequencing (ATAC–seq) assays for chromatin accessibility across 72 distinct tissue-stages. We used integrative analysis to develop a unified set of chromatin state annotations, infer the identities of dynamic enhancers and key transcriptional regulators, and characterize the relationship between chromatin state and accessibility during developmental gene regulation. We also leveraged these data to link enhancers to putative target genes and demonstrate tissue-specific enrichments of sequence variants associated with disease in humans. The mouse ENCODE data sets provide a compendium of resources for biomedical researchers and achieve, to our knowledge, the most comprehensive view of chromatin dynamics during mammalian fetal development to date

Landscape of transcription in human cells

Eukaryotic cells make many types of primary and processed RNAs that are found either in specific subcellular compartments or throughout the cells. A complete catalogue of these RNAs is not yet available and their characteristic subcellular localizations are also poorly understood. Because RNA represents the direct output of the genetic information encoded by genomes and a significant proportion of a cell’s regulatory capabilities are focused on its synthesis, processing, transport, modification and translation, the generation of such a catalogue is crucial for understanding genome function. Here we report evidence that three-quarters of the human genome is capable of being transcribed, as well as observations about the range and levels of expression, localization, processing fates, regulatory regions and modifications of almost all currently annotated and thousands of previously unannotated RNAs. These observations, taken together, prompt a redefinition of the concept of a gene

A comparative encyclopedia of DNA elements in the mouse genome

The laboratory mouse shares the majority of its protein-coding genes with humans, making it the premier model organism in biomedical research, yet the two mammals differ in significant ways. To gain greater insights into both shared and species-specific transcriptional and cellular regulatory programs in the mouse, the Mouse ENCODE Consortium has mapped transcription, DNase I hypersensitivity, transcription factor binding, chromatin modifications and replication domains throughout the mouse genome in diverse cell and tissue types. By comparing with the human genome, we not only confirm substantial conservation in the newly annotated potential functional sequences, but also find a large degree of divergence of sequences involved in transcriptional regulation, chromatin state and higher order chromatin organization. Our results illuminate the wide range of evolutionary forces acting on genes and their regulatory regions, and provide a general resource for research into mammalian biology and mechanisms of human diseases

A User's Guide to the Encyclopedia of DNA Elements (ENCODE)

The mission of the Encyclopedia of DNA Elements (ENCODE) Project is to enable the scientific and medical communities to interpret the human genome sequence and apply it to understand human biology and improve health. The ENCODE Consortium is integrating multiple technologies and approaches in a collective effort to discover and define the functional elements encoded in the human genome, including genes, transcripts, and transcriptional regulatory regions, together with their attendant chromatin states and DNA methylation patterns. In the process, standards to ensure high-quality data have been implemented, and novel algorithms have been developed to facilitate analysis. Data and derived results are made available through a freely accessible database. Here we provide an overview of the project and the resources it is generating and illustrate the application of ENCODE data to interpret the human genome