Communicability and multipartite structures in complex networks at negative absolute temperatures

A Developing Symbiosis: Enabling Cross-Talk Between Ecologists and Microbiome Scientists

Like all interactions, the success of cross-discipline collaborations relies on effective communication. Ecology offers theoretical frameworks and lexicons to study microbiomes. Yet some of the terms and concepts borrowed from ecology are being used discordantly by microbiome studies from their traditional definitions. Here we define some of the ecological terms and concepts as they are used in ecology and the study of microbiomes. Where applicable, we have provided the historical context of the terms, highlighted examples from microbiome studies, and considered the research methods involved. We divided these concepts into four sections: Biomes, Diversity, Symbiosis, and Succession. Biomes encompass the interactions within the biotic and abiotic features of an environment. This extends to the term "microbiome," derived from "biome," and includes an environment and all the microbes within it. Diversity encompasses patterns of species richness, abundance, and biogeography, all of which are important to understanding the distribution of microbiomes. Symbiosis emphasizes the relationships between organisms within a community. Symbioses are often misunderstood to be synonymous with mutualism. We discard that implication, in favor of a broader, more historically accurate definition which spans the continuum from parasitism to mutualism. Succession includes classical succession, alternative stable states, community assembly frameworks, and r/K-selection. Our hope is that as microbiome researchers continue to apply ecological terms, and as ecologists continue to gain interest in microbiomes, each will do so in a way that enables cross-talk between them. We recommend initiating these collaborations by using a common lexicon, from which new concepts can emerge.

Spectral algorithms for heterogeneous biological networks

Spectral methods, which use information relating to eigenvectors, singular vectors and generalized singular vectors, help us to visualize and summarize sets of pairwise interactions. In this work, we motivate and discuss the use of spectral methods by taking a matrix computation view and applying concepts from applied linear algebra. We show that this unified approach is sufficiently flexible to allow multiple sources of network information to be combined. We illustrate the methods on microarray data arising from a large population-based study in human adipose tissue, combined with related information concerning metabolic pathways.

Complex networks in the Euclidean space of communicability distances

We study the properties of complex networks embedded in a Euclidean space of communicability distances. The communicability distance between two nodes is defined as the difference between the weighted sum of walks self-returning to the nodes and the weighted sum of walks going from one node to the other. We give some indications that the communicability distance identifies the least crowded routes in networks where simultaneous submission of packages is taking place. We define an index Q based on communicability and shortest path distances, which allows reinterpreting the "small-world" phenomenon as the region of minimum Q in the Watts-Strogatz model. It also allows the classification and analysis of networks with different efficiency of spatial uses. Consequently, the communicability distance displays unique features for the analysis of complex networks in different scenarios.

Exploring metabolic pathway disruption in the subchronic phencyclidine model of schizophrenia with the Generalized Singular Value Decomposition

BACKGROUND

The quantification of experimentally-induced alterations in biological pathways remains a major challenge in systems biology. One example of this is the quantitative characterization of alterations in defined, established metabolic pathways from complex metabolomic data. At present, the disruption of a given metabolic pathway is inferred from metabolomic data by observing an alteration in the level of one or more individual metabolites present within that pathway. Not only is this approach open to subjectivity, as metabolites participate in multiple pathways, but it also ignores useful information available through the pairwise correlations between metabolites. This extra information may be incorporated using a higher-level approach that looks for alterations between a pair of correlation networks. In this way experimentally-induced alterations in metabolic pathways can be quantitatively defined by characterizing group differences in metabolite clustering. Taking this approach increases the objectivity of interpreting alterations in metabolic pathways from metabolomic data.

RESULTS

We present and justify a new technique for comparing pairs of networks--in our case these networks are based on the same set of nodes and there are two distinct types of weighted edges. The algorithm is based on the Generalized Singular Value Decomposition (GSVD), which may be regarded as an extension of Principle Components Analysis to the case of two data sets. We show how the GSVD can be interpreted as a technique for reordering the two networks in order to reveal clusters that are exclusive to only one. Here we apply this algorithm to a new set of metabolomic data from the prefrontal cortex (PFC) of a translational model relevant to schizophrenia, rats treated subchronically with the N-methyl-D-Aspartic acid (NMDA) receptor antagonist phencyclidine (PCP). This provides us with a means to quantify which predefined metabolic pathways (Kyoto Encyclopedia of Genes and Genomes (KEGG) metabolite pathway database) were altered in the PFC of PCP-treated rats. Several significant changes were discovered, notably: 1) neuroactive ligands active at glutamate and GABA receptors are disrupted in the PFC of PCP-treated animals, 2) glutamate dysfunction in these animals was not limited to compromised glutamatergic neurotransmission but also involves the disruption of metabolic pathways linked to glutamate; and 3) a specific series of purine reactions Xanthine ← Hypoxyanthine ↔ Inosine ← IMP → adenylosuccinate is also disrupted in the PFC of PCP-treated animals.

CONCLUSIONS

Network reordering via the GSVD provides a means to discover statistically validated differences in clustering between a pair of networks. In practice this analytical approach, when applied to metabolomic data, allows us to quantify the alterations in metabolic pathways between two experimental groups. With this new computational technique we identified metabolic pathway alterations that are consistent with known results. Furthermore, we discovered disruption in a novel series of purine reactions that may contribute to the PFC dysfunction and cognitive deficits seen in schizophrenia.