The Dali Domain Dictionary (http://www.ebi.ac.uk/dali/domain) is a numerical taxonomy of all known structures in the Protein Data Bank (PDB). The taxonomy is derived fully automatically from measurements of structural, functional and sequence similarities. Here, we report the extension of the classification to match the traditional four hierarchical levels corresponding to: (i) supersecondary structural motifs (attractors in fold space), (ii) the topology of globular domains (fold types), (iii) remote homologues (functional families) and (iv) homologues with sequence identity above 25% (sequence families). The computational definitions of attractors and functional families are new. In September 2000, the Dali classification contained 10 531 PDB entries comprising 17 101 chains, which were partitioned into five attractor regions, 1375 fold types, 2582 functional families and 3724 domain sequence families. Sequence families were further associated with 99 582 unique homologous sequences in the HSSP database, which increases the number of effectively known structures several-fold. The resulting database contains the description of protein domain architecture, the definition of structural neighbours around each known structure, the definition of structurally conserved cores and a comprehensive library of explicit multiple alignments of distantly related protein families.
Next-generation sequencing (NGS) has made it possible to determine the sequence and relative abundance of all nucleotides in a biological or environmental sample. Today, NGS is routinely used to understand many important topics in biology from human disease to microorganism diversity. A cornerstone of NGS is the quantification of RNA or DNA presence as counts. However, these counts are not counts per se: the magnitude of the counts are determined arbitrarily by the sequencing depth, not by the input material. Consequently, counts must undergo normalization prior to use. Conventional normalization methods require a set of assumptions: they assume that the majority of features are unchanged, and that all environments under study have the same carrying capacity for nucleotide synthesis. These assumptions are often untestable and may not hold when comparing heterogeneous samples (e.g., samples collected across distinct cancers or tissues). Instead, methods developed within the field of compositional data analysis offer a general solution that is assumption-free and valid for all data. In this manuscript, we synthesize the extant literature to provide a concise guide on how to apply compositional data analysis to NGS count data. In doing so, we review zero replacement, differential abundance analysis, and within-group and between-group coordination analysis. We then discuss how this pipeline can accommodate complex study design, facilitate the analysis of vertically and horizontally integrated data, including multiomics data, and further extend to single-cell sequencing data. In highlighting the limitations of total library size, effective library size, and spike-in normalizations, we propose the log-ratio transformation as a general solution to answer the question, "Relative to some important activity of the cell, what is changing?". Taken together, this manuscript establishes the first fully comprehensive analysis protocol that is suitable for any and all -omics data.
Gene expression data, such as those generated by next generation sequencing technologies (RNA-seq), are of an inherently relative nature: the total number of sequenced reads has no biological meaning. This issue is most often addressed with various normalization techniques which all face the same problem: once information about the total mRNA content of the origin cells is lost, it cannot be recovered by mere technical means. Additional knowledge, in the form of an unchanged reference, is necessary; however, this reference can usually only be estimated. Here we propose a novel method where sample normalization is unnecessary, but important insights can be obtained nevertheless. Instead of trying to recover absolute abundances, our method is entirely based on ratios, so normalization factors cancel by default. Although the differential expression of individual genes cannot be recovered this way, the ratios themselves can be differentially expressed (even when their constituents are not). Yet, most current analyses are blind to these cases, while our approach reveals them directly. Specifically, we show how the differential expression of gene ratios can be formalized by decomposing log-ratio variance (LRV) and deriving intuitive statistics from it. Although small LRVs have been used to detect proportional genes in gene expression data before, we focus here on the change in proportionality factors between groups of samples (e.g. tissue-specific proportionality). For this, we propose a statistic that is equivalent to the squared t-statistic of one-way ANOVA, but for gene ratios. In doing so, we show how precision weights can be incorporated to account for the peculiarities of count data, and, moreover, how a moderated statistic can be derived in the same way as the one following from a hierarchical model for individual genes. We also discuss approaches to deal with zero counts, deriving an expression of our statistic that is able to incorporate them. In providing a detailed analysis of the connections between the differential expression of genes and the differential proportionality of pairs, we facilitate a clear interpretation of new concepts. The proposed framework is applied to a data set from GTEx consisting of 98 samples from the cerebellum and cortex, with selected examples shown. A computationally efficient implementation of the approach in R has been released as an addendum to the propr package. 1
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