On the origin of distribution patterns of motifs in biological networks

<p>Abstract</p> <p>Background</p> <p>Inventories of small subgraphs in biological networks have identified commonly-recurring patterns, called motifs. The inference that these motifs have been selected for function rests on the idea that their occurrences are significantly more frequent than random.</p> <p>Results</p> <p>Our analysis of several large biological networks suggests, in contrast, that the frequencies of appearance of common subgraphs are similar in natural and corresponding random networks.</p> <p>Conclusion</p> <p>Indeed, certain topological features of biological networks give rise naturally to the common appearance of the motifs. We therefore question whether frequencies of occurrences are reasonable evidence that the structures of motifs have been selected for their functional contribution to the operation of networks.</p

A fast indexing approach for protein structure comparison

BACKGROUND: Protein structure comparison is a fundamental task in structural biology. While the number of known protein structures has grown rapidly over the last decade, searching a large database of protein structures is still relatively slow using existing methods. There is a need for new techniques which can rapidly compare protein structures, whilst maintaining high matching accuracy. RESULTS: We have developed IR Tableau, a fast protein comparison algorithm, which leverages the tableau representation to compare protein tertiary structures. IR tableau compares tableaux using information retrieval style feature indexing techniques. Experimental analysis on the ASTRAL SCOP protein structural domain database demonstrates that IR Tableau achieves two orders of magnitude speedup over the search times of existing methods, while producing search results of comparable accuracy. CONCLUSION: We show that it is possible to obtain very significant speedups for the protein structure comparison problem, by employing an information retrieval style approach for indexing proteins. The comparison accuracy achieved is also strong, thus opening the way for large scale processing of very large protein structure databases

How precise are reported protein coordinate data?

Atomic coordinates in the Worldwide Protein Data Bank (wwPDB) are generally reported to greater precision than the experimental structure determinations have actually achieved. By using information theory and data compression to study the compressibility of protein atomic coordinates, it is possible to quantify the amount of randomness in the coordinate data and thereby to determine the realistic precision of the reported coordinates. On average, the value of each Cα coordinate in a set of selected protein structures solved at a variety of resolutions is good to about 0.1 Å

The divergence time of protein structures modelled by Markov matrices and its relation to the divergence of sequences

A complete time-parameterized statistical model quantifying the divergent evolution of protein structures in terms of the patterns of conservation of their secondary structures is inferred from a large collection of protein 3D structure alignments. This provides a better alternative to time-parameterized sequence-based models of protein relatedness, that have clear limitations dealing with twilight and midnight zones of sequence relationships. Since protein structures are far more conserved due to the selection pressure directly placed on their function, divergence time estimates can be more accurate when inferred from structures. We use the Bayesian and information-theoretic framework of Minimum Message Length to infer a time-parameterized stochastic matrix (accounting for perturbed structural states of related residues) and associated Dirichlet models (accounting for insertions and deletions during the evolution of protein domains). These are used in concert to estimate the Markov time of divergence of tertiary structures, a task previously only possible using proxies (like RMSD). By analyzing one million pairs of homologous structures, we yield a relationship between the Markov divergence time of structures and of sequences. Using these inferred models and the relationship between the divergence of sequences and structures, we demonstrate a competitive performance in secondary structure prediction against neural network architectures commonly employed for this task. The source code and supplementary information are downloadable from \url{http://lcb.infotech.monash.edu.au/sstsum}.Comment: 12 pages, 6 figure

Efficient large-scale protein sequence comparison and gene matching to identify orthologs and co-orthologs

Broadly, computational approaches for ortholog assignment is a three steps process: (i) identify all putative homologs between the genomes, (ii) identify gene anchors and (iii) link anchors to identify best gene matches given their order and context. In this article, we engineer two methods to improve two important aspects of this pipeline [specifically steps (ii) and (iii)]. First, computing sequence similarity data [step (i)] is a computationally intensive task for large sequence sets, creating a bottleneck in the ortholog assignment pipeline. We have designed a fast and highly scalable sort-join method (afree) based on k-mer counts to rapidly compare all pairs of sequences in a large protein sequence set to identify putative homologs. Second, availability of complex genomes containing large gene families with prevalence of complex evolutionary events, such as duplications, has made the task of assigning orthologs and co-orthologs difficult. Here, we have developed an iterative graph matching strategy where at each iteration the best gene assignments are identified resulting in a set of orthologs and co-orthologs. We find that the afree algorithm is faster than existing methods and maintains high accuracy in identifying similar genes. The iterative graph matching strategy also showed high accuracy in identifying complex gene relationships. Standalone afree available from http://vbc.med.monash.edu.au/∼kmahmood/afree. EGM2, complete ortholog assignment pipeline (including afree and the iterative graph matching method) available from http://vbc.med.monash.edu.au/∼kmahmood/EGM2

Bridging the gaps in statistical models of protein alignment

SUMMARY: Sequences of proteins evolve by accumulating substitutions together with insertions and deletions (indels) of amino acids. However, it remains a common practice to disconnect substitutions and indels, and infer approximate models for each of them separately, to quantify sequence relationships. Although this approach brings with it computational convenience (which remains its primary motivation), there is a dearth of attempts to unify and model them systematically and together. To overcome this gap, this article demonstrates how a complete statistical model quantifying the evolution of pairs of aligned proteins can be constructed using a time-parameterized substitution matrix and a time-parameterized alignment state machine. Methods to derive all parameters of such a model from any benchmark collection of aligned protein sequences are described here. This has not only allowed us to generate a unified statistical model for each of the nine widely used substitution matrices (PAM, JTT, BLOSUM, JO, WAG, VTML, LG, MIQS and PFASUM), but also resulted in a new unified model, MMLSUM. Our underlying methodology measures the Shannon information content using each model to explain losslessly any given collection of alignments, which has allowed us to quantify the performance of all the above models on six comprehensive alignment benchmarks. Our results show that MMLSUM results in a new and clear overall best performance, followed by PFASUM, VTML, BLOSUM and MIQS, respectively, amongst the top five. We further analyze the statistical properties of MMLSUM model and contrast it with others. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online