Singular value decomposition analysis of protein sequence alignment score data

A singular value decomposition approach for improved taxonomic classification of biological sequences

Background

Singular value decomposition (SVD) is a powerful technique for information retrieval; it helps uncover relationships between elements that are not prima facie related. SVD was initially developed to reduce the time needed for information retrieval and analysis of very large data sets in the complex internet environment. Since information retrieval from large-scale genome and proteome data sets has a similar level of complexity, SVD-based methods could also facilitate data analysis in this research area.

Results

We found that SVD applied to amino acid sequences demonstrates relationships and provides a basis for producing clusters and cladograms, demonstrating evolutionary relatedness of species that correlates well with Linnaean taxonomy. The choice of a reasonable number of singular values is crucial for SVD-based studies. We found that fewer singular values are needed to produce biologically significant clusters when SVD is employed. Subsequently, we developed a method to determine the lowest number of singular values and fewest clusters needed to guarantee biological significance; this system was developed and validated by comparison with Linnaean taxonomic classification.

Conclusions

By using SVD, we can reduce uncertainty concerning the appropriate rank value necessary to perform accurate information retrieval analyses. In tests, clusters that we developed with SVD perfectly matched what was expected based on Linnaean taxonomy.

Amino acid "little Big Bang": representing amino acid substitution matrices as dot products of Euclidian vectors

BACKGROUND

Sequence comparisons make use of a one-letter representation for amino acids, the necessary quantitative information being supplied by the substitution matrices. This paper deals with the problem of finding a representation that provides a comprehensive description of amino acid intrinsic properties consistent with the substitution matrices.

RESULTS

We present a Euclidian vector representation of the amino acids, obtained by the singular value decomposition of the substitution matrices. The substitution matrix entries correspond to the dot product of amino acid vectors. We apply this vector encoding to the study of the relative importance of various amino acid physicochemical properties upon the substitution matrices. We also characterize and compare the PAM and BLOSUM series substitution matrices.

CONCLUSIONS

This vector encoding introduces a Euclidian metric in the amino acid space, consistent with substitution matrices. Such a numerical description of the amino acid is useful when intrinsic properties of amino acids are necessary, for instance, building sequence profiles or finding consensus sequences, using machine learning algorithms such as Support Vector Machine and Neural Networks algorithms.

Subfamily specific conservation profiles for proteins based on n-gram patterns

Background

A new algorithm has been developed for generating conservation profiles that reflect the evolutionary history of the subfamily associated with a query sequence. It is based on n-gram patterns (NP{n,m}) which are sets of n residues and m wildcards in windows of size n+m. The generation of conservation profiles is treated as a signal-to-noise problem where the signal is the count of n-gram patterns in target sequences that are similar to the query sequence and the noise is the count over all target sequences. The signal is differentiated from the noise by applying singular value decomposition to sets of target sequences rank ordered by similarity with respect to the query.

Results

The new algorithm was used to construct 4,248 profiles from 120 randomly selected Pfam-A families. These were compared to profiles generated from multiple alignments using the consensus approach. The two profiles were similar whenever the subfamily associated with the query sequence was well represented in the multiple alignment. It was possible to construct subfamily specific conservation profiles using the new algorithm for subfamilies with as few as five members. The speed of the new algorithm was comparable to the multiple alignment approach.

Conclusion

Subfamily specific conservation profiles can be generated by the new algorithm without aprioi knowledge of family relationships or domain architecture. This is useful when the subfamily contains multiple domains with different levels of representation in protein databases. It may also be applicable when the subfamily sample size is too small for the multiple alignment approach.

Probabilistic assembly of human protein interaction networks from label-free quantitative proteomics

Large-scale affinity purification and mass spectrometry studies have played important roles in the assembly and analysis of comprehensive protein interaction networks for lower eukaryotes. However, the development of such networks for human proteins has been slowed by the high cost and significant technical challenges associated with systematic studies of protein interactions. To address this challenge, we have developed a method for building local and focused networks. This approach couples vector algebra and statistical methods with normalized spectral counting (NSAF) derived from the analysis of affinity purifications via chromatography-based proteomics. After mathematical removal of contaminant proteins, the core components of multiprotein complexes are determined by singular value decomposition analysis and clustering. The probability of interactions within and between complexes is computed solely based upon NSAFs using Bayes' approach. To demonstrate the application of this method to small-scale datasets, we analyzed an expanded human TIP49a and TIP49b dataset. This dataset contained proteins affinity-purified with 27 different epitope-tagged components of the chromatin remodeling SRCAP, hINO80, and TRRAP/TIP60 complexes, and the nutrient sensing complex Uri/Prefoldin. Within a core network of 65 unique proteins, we captured all known components of these complexes and novel protein associations, especially in the Uri/Prefoldin complex. Finally, we constructed a probabilistic human interaction network composed of 557 protein pairs.