Flexible construction of hierarchical scale-free networks with general exponent

Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model which reproduces the main experimental properties observed in real networks: scale-free of degree distribution $P(k)$ (frequency of the nodes that are connected to $k$ other nodes decays as a power-law $P(k)\sim k^{-\gamma}$) and power-law scaling of the clustering coefficient $C(k)\sim k^{-1}$. The major novelties of our model can be summarized as follows: {\it (a)} The model generates networks with scale-free distribution for the degree of nodes with general exponent $\gamma > 2$, and arbitrarily close to any specified value, being able to reproduce most of the observed hierarchical scale-free topologies. In contrast, previous models can not obtain values of $\gamma > 2.58$. {\it (b)} Our model has structural flexibility because {\it (i)} it can incorporate various types of basic building blocks (e.g., triangles, tetrahedrons and, in general, fully connected clusters of $n$ nodes) and {\it (ii)} it allows a large variety of configurations (i.e., the model can use more than $n-1$ copies of basic blocks of $n$ nodes). The structural features of our proposed model might lead to a better understanding of architectures of biological and non-biological networks.Comment: RevTeX, 5 pages, 4 figure

MACiE: a database of enzyme reaction mechanisms.

SUMMARY: MACiE (mechanism, annotation and classification in enzymes) is a publicly available web-based database, held in CMLReact (an XML application), that aims to help our understanding of the evolution of enzyme catalytic mechanisms and also to create a classification system which reflects the actual chemical mechanism (catalytic steps) of an enzyme reaction, not only the overall reaction. AVAILABILITY: http://www-mitchell.ch.cam.ac.uk/macie/.EPSRC (G.L.H. and J.B.O.M.), the BBSRC (G.J.B. and J.M.T.—CASE studentship in association with Roche Products Ltd; N.M.O.B. and J.B.O.M.—grant BB/C51320X/1), the Chilean Government’s Ministerio de Planificacio´n y Cooperacio´n and Cambridge Overseas Trust (D.E.A.) for funding and Unilever for supporting the Centre for Molecular Science Informatics.application note restricted to 2 printed pages web site: http://www-mitchell.ch.cam.ac.uk/macie

Elliptic Calogero-Moser Systems and Isomonodromic Deformations

We show that various models of the elliptic Calogero-Moser systems are accompanied with an isomonodromic system on a torus. The isomonodromic partner is a non-autonomous Hamiltonian system defined by the same Hamiltonian. The role of the time variable is played by the modulus of the base torus. A suitably chosen Lax pair (with an elliptic spectral parameter) of the elliptic Calogero-Moser system turns out to give a Lax representation of the non-autonomous system as well. This Lax representation ensures that the non-autonomous system describes isomonodromic deformations of a linear ordinary differential equation on the torus on which the spectral parameter of the Lax pair is defined. A particularly interesting example is the ``extended twisted $BC_\ell$ model'' recently introduced along with some other models by Bordner and Sasaki, who remarked that this system is equivalent to Inozemtsev's generalized elliptic Calogero-Moser system. We use the ``root type'' Lax pair developed by Bordner et al. to formulate the associated isomonodromic system on the torus.Comment: latex2e using amsfonts package, 50pages; (v2) typos corrected; (v3) typos in (3.35), (3.46), (3.48) and (B.26) corrected; (v4) errors in (1.7),(1.12),(3.46),(3.47) and (3.48) corrected; (v5) final version for publication, errors in (2.31),(2.35),(3.12),(3.30),(3.45),(4.16) and (4.37) correcte

mzMatch-ISO: an R tool for the annotation and relative quantification of isotope-labelled mass spectrometry data

<p>Motivation: Stable isotope-labelling experiments have recently gained increasing popularity in metabolomics studies, providing unique insights into the dynamics of metabolic fluxes, beyond the steady-state information gathered by routine mass spectrometry. However, most liquid chromatography–mass spectrometry data analysis software lacks features that enable automated annotation and relative quantification of labelled metabolite peaks. Here, we describe mzMatch–ISO, a new extension to the metabolomics analysis pipeline mzMatch.R.</p> <p>Results: Targeted and untargeted isotope profiling using mzMatch–ISO provides a convenient visual summary of the quality and quantity of labelling for every metabolite through four types of diagnostic plots that show (i) the chromatograms of the isotope peaks of each compound in each sample group; (ii) the ratio of mono-isotopic and labelled peaks indicating the fraction of labelling; (iii) the average peak area of mono-isotopic and labelled peaks in each sample group; and (iv) the trend in the relative amount of labelling in a predetermined isotopomer. To aid further statistical analyses, the values used for generating these plots are also provided as a tab-delimited file. We demonstrate the power and versatility of mzMatch–ISO by analysing a 13C-labelled metabolome dataset from trypanosomal parasites.</p&gt

mzMatch-ISO: an R tool for the annotation and relative quantification of isotope-labelled mass spectrometry data

<p>Motivation: Stable isotope-labelling experiments have recently gained increasing popularity in metabolomics studies, providing unique insights into the dynamics of metabolic fluxes, beyond the steady-state information gathered by routine mass spectrometry. However, most liquid chromatography–mass spectrometry data analysis software lacks features that enable automated annotation and relative quantification of labelled metabolite peaks. Here, we describe mzMatch–ISO, a new extension to the metabolomics analysis pipeline mzMatch.R.</p> <p>Results: Targeted and untargeted isotope profiling using mzMatch–ISO provides a convenient visual summary of the quality and quantity of labelling for every metabolite through four types of diagnostic plots that show (i) the chromatograms of the isotope peaks of each compound in each sample group; (ii) the ratio of mono-isotopic and labelled peaks indicating the fraction of labelling; (iii) the average peak area of mono-isotopic and labelled peaks in each sample group; and (iv) the trend in the relative amount of labelling in a predetermined isotopomer. To aid further statistical analyses, the values used for generating these plots are also provided as a tab-delimited file. We demonstrate the power and versatility of mzMatch–ISO by analysing a 13C-labelled metabolome dataset from trypanosomal parasites.</p&gt

Gene3D: comprehensive structural and functional annotation of genomes

Gene3D provides comprehensive structural and functional annotation of most available protein sequences, including the UniProt, RefSeq and Integr8 resources. The main structural annotation is generated through scanning these sequences against the CATH structural domain database profile-HMM library. CATH is a database of manually derived PDB-based structural domains, placed within a hierarchy reflecting topology, homology and conservation and is able to infer more ancient and divergent homology relationships than sequence-based approaches. This data is supplemented with Pfam-A, other non-domain structural predictions (i.e. coiled coils) and experimental data from UniProt. In order to enhance the investigations possible with this data, we have also incorporated a variety of protein annotation resources, including protein–protein interaction data, GO functional assignments, KEGG pathways, FUNCAT functional descriptions and links to microarray expression data. All of this data can be accessed through a newly re-designed website that has a focus on flexibility and clarity, with searches that can be restricted to a single genome or across the entire sequence database. Currently Gene3D contains over 3.5 million domain assignments for nearly 5 million proteins including 527 completed genomes. This is available at: http://gene3d.biochem.ucl.ac.uk

Software that goes with the flow in systems biology

A recent article in BMC Bioinformatics describes new advances in workflow systems for computational modeling in systems biology. Such systems can accelerate, and improve the consistency of, modeling through automation not only at the simulation and results-production stages, but also at the model-generation stage. Their work is a harbinger of the next generation of more powerful software for systems biologists

A statistical mechanics description of environmental variability in metabolic networks

Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks display considerable asymmetry. In this paper, we explore possible evolutionary factors pertaining to the reduced symmetry observed in these networks, and demonstrate the important role environmental variability plays in shaping their structural organization. Interpreting the returnability index as an equilibrium constant for a reaction network in equilibrium with a hypothetical reference system, enables us to quantify the extent to which a metabolic network is in disequilibrium. Further, by introducing a new directed centrality measure via an extension of the subgraph centrality metric to directed networks, we are able to characterise individual metabolites by their participation within metabolic pathways. To demonstrate these ideas, we study 116 metabolic networks of bacteria. In particular, we find that the equilibrium constant for the metabolic networks decreases significantly in-line with variability in bacterial habitats, supporting the view that environmental variability promotes disequilibrium within these biochemical reaction system

Application of regulatory sequence analysis and metabolic network analysis to the interpretation of gene expression data

We present two complementary approaches for the interpretation of clusters of co-regulated genes, such as those obtained from DNA chips and related methods. Starting from a cluster of genes with similar expression profiles, two basic questions can be asked: 1. Which mechanism is responsible for the coordinated transcriptional response of the genes? This question is approached by extracting motifs that are shared between the upstream sequences of these genes. The motifs extracted are putative cis-acting regulatory elements. 2. What is the physiological meaning for the cell to express together these genes? One way to answer the question is to search for potential metabolic pathways that could be catalyzed by the products of the genes. This can be done by selecting the genes from the cluster that code for enzymes, and trying to assemble the catalyzed reactions to form metabolic pathways. We present tools to answer these two questions, and we illustrate their use with selected examples in the yeast Saccharomyces cerevisiae. The tools are available on the web (http://ucmb.ulb.ac.be/bioinformatics/rsa-tools/; http://www.ebi.ac.uk/research/pfbp/; http://www.soi.city.ac.uk/~msch/)