Transition Matrix Theory

In this article we present a unification of the theory of algebraic, singular, topological and directional transition matrices by introducing the (generalized) transition matrix which encompasses each of the previous four. Some transition matrix existence results are presented as well as verification that each of the previous transition matrices are cases of the generalized transition matrix. Furthermore we address how applications of the previous transition matrices to the Conley Index theory carry over to the generalized transition matrix

Relating the metatranscriptome and metagenome of the human gut

Although the composition of the human microbiome is now wellstudied, the microbiota’s \u3e8 million genes and their regulation remain largely uncharacterized. This knowledge gap is in part because of the difficulty of acquiring large numbers of samples amenable to functional studies of the microbiota. We conducted what is, to our knowledge, one of the first human microbiome studies in a well-phenotyped prospective cohort incorporating taxonomic, metagenomic, and metatranscriptomic profiling at multiple body sites using self-collected samples. Stool and saliva were provided by eight healthy subjects, with the former preserved by three different methods (freezing, ethanol, and RNAlater) to validate self-collection. Within-subject microbial species, gene, and transcript abundances were highly concordant across sampling methods, with only a small fraction of transcripts (\u3c5%) displaying between-method variation. Next, we investigated relationships between the oral and gut microbial communities, identifying a subset of abundant oral microbes that routinely survive transit to the gut, but with minimal transcriptional activity there. Finally, systematic comparison of the gut metagenome and metatranscriptome revealed that a substantial fraction (41%) of microbial transcripts were not differentially regulated relative to their genomic abundances. Of the remainder, consistently underexpressed pathways included sporulation and amino acid biosynthesis, whereas up-regulated pathways included ribosome biogenesis and methanogenesis. Across subjects, metatranscriptional profiles were significantly more individualized than DNA-level functional profiles, but less variable than microbial composition, indicative of subject-specific whole-community regulation. The results thus detail relationships between community genomic potential and gene expression in the gut, and establish the feasibility of metatranscriptomic investigations in subject-collected and shipped samples

Species-level functional profiling of metagenomes and metatranscriptomes.

Functional profiles of microbial communities are typically generated using comprehensive metagenomic or metatranscriptomic sequence read searches, which are time-consuming, prone to spurious mapping, and often limited to community-level quantification. We developed HUMAnN2, a tiered search strategy that enables fast, accurate, and species-resolved functional profiling of host-associated and environmental communities. HUMAnN2 identifies a community's known species, aligns reads to their pangenomes, performs translated search on unclassified reads, and finally quantifies gene families and pathways. Relative to pure translated search, HUMAnN2 is faster and produces more accurate gene family profiles. We applied HUMAnN2 to study clinal variation in marine metabolism, ecological contribution patterns among human microbiome pathways, variation in species' genomic versus transcriptional contributions, and strain profiling. Further, we introduce 'contributional diversity' to explain patterns of ecological assembly across different microbial community types

Multi-omics of the gut microbial ecosystem in inflammatory bowel diseases.

Inflammatory bowel diseases, which include Crohn's disease and ulcerative colitis, affect several million individuals worldwide. Crohn's disease and ulcerative colitis are complex diseases that are heterogeneous at the clinical, immunological, molecular, genetic, and microbial levels. Individual contributing factors have been the focus of extensive research. As part of the Integrative Human Microbiome Project (HMP2 or iHMP), we followed 132 subjects for one year each to generate integrated longitudinal molecular profiles of host and microbial activity during disease (up to 24 time points each; in total 2,965 stool, biopsy, and blood specimens). Here we present the results, which provide a comprehensive view of functional dysbiosis in the gut microbiome during inflammatory bowel disease activity. We demonstrate a characteristic increase in facultative anaerobes at the expense of obligate anaerobes, as well as molecular disruptions in microbial transcription (for example, among clostridia), metabolite pools (acylcarnitines, bile acids, and short-chain fatty acids), and levels of antibodies in host serum. Periods of disease activity were also marked by increases in temporal variability, with characteristic taxonomic, functional, and biochemical shifts. Finally, integrative analysis identified microbial, biochemical, and host factors central to this dysregulation. The study's infrastructure resources, results, and data, which are available through the Inflammatory Bowel Disease Multi'omics Database ( http://ibdmdb.org ), provide the most comprehensive description to date of host and microbial activities in inflammatory bowel diseases

Modal Logics of Topological Relations

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to highly undecidable, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity

Structure and Age Jointly Influence Rates of Protein Evolution

What factors determine a protein's rate of evolution are actively debated. Especially unclear is the relative role of intrinsic factors of present-day proteins versus historical factors such as protein age. Here we study the interplay of structural properties and evolutionary age, as determinants of protein evolutionary rate. We use a large set of one-to-one orthologs between human and mouse proteins, with mapped PDB structures. We report that previously observed structural correlations also hold within each age group – including relationships between solvent accessibility, designabililty, and evolutionary rates. However, age also plays a crucial role: age modulates the relationship between solvent accessibility and rate. Additionally, younger proteins, despite being less designable, tend to evolve faster than older proteins. We show that previously reported relationships between age and rate cannot be explained by structural biases among age groups. Finally, we introduce a knowledge-based potential function to study the stability of proteins through large-scale computation. We find that older proteins are more stable for their native structure, and more robust to mutations, than younger ones. Our results underscore that several determinants, both intrinsic and historical, can interact to determine rates of protein evolution

Comparative genomics and genome biology of Campylobacter showae

We thank the Garrett and Huttenhower laboratories for useful discussions. This work was supported by a Fulbright Scholarship to GH, an NHS Grampian Endowment grant fund to I.M. and G.H., a CSO clinical academic fellowship to R.H. (CAF/08/01). RH is supported by an NHS Research Scotland Career Researcher Fellowship. NIH NIDDK grant R24DK110499 to CH, and NSF grant DBI-1053486 to CH.Peer reviewedPublisher PD