Peptide vocabulary analysis reveals ultra-conservation and homonymity in protein sequences

A new algorithm is presented for vocabulary analysis (word detection) in texts of human origin. It performs at 60%–70% overall accuracy and greater than 80% accuracy for longer words, and approximately 85% sensitivity on Alice in Wonderland, a considerable improvement on previous methods. When applied to protein sequences, it detects short sequences analogous to words in human texts, i.e. intolerant to changes in spelling (mutation), and relatively contextindependent in their meaning (function). Some of these are homonyms of up to 7 amino acids, which can assume different structures in different proteins. Others are ultra-conserved stretches of up to 18 amino acids within proteins of less than 40% overall identity, reflecting extreme constraint or convergent evolution. Different species are found to have qualitatively different major peptide vocabularies, e.g. some are dominated by large gene families, while others are rich in simple repeats or dominated by internally repetitive proteins. This suggests the possibility of a peptide vocabulary signature, analogous to genome signatures in DNA. Homonyms may be useful in detecting convergent evolution and positive selection in protein evolution. Ultra-conserved words may be useful in identifying structures intolerant to substitution over long periods of evolutionary time

Locating regions in a sequence under density constraints

Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence matching. Mathematically, this corresponds to searching a string of 0s and 1s for a substring whose relative proportion of 1s lies between given lower and upper bounds. We consider the algorithmic problem of locating the longest such substring, as well as other related problems (such as finding the shortest substring or a maximal set of disjoint substrings). For locating the longest such substring, we develop an algorithm that runs in O(n) time, improving upon the previous best-known O(n log n) result. For the related problems we develop O(n log log n) algorithms, again improving upon the best-known O(n log n) results. Practical testing verifies that our new algorithms enjoy significantly smaller time and memory footprints, and can process sequences that are orders of magnitude longer as a result.Comment: 17 pages, 8 figures; v2: minor revisions, additional explanations; to appear in SIAM Journal on Computin

Measure representation and multifractal analysis of complete genomes

This paper introduces the notion of measure representation of DNA sequences. Spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes. The main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria. From the measure representations and the values of the $D_{q}$ spectra and related $C_{q}$ curves, it is concluded that these complete genomes are not random sequences. In fact, spectral analyses performed indicate that these measure representations considered as time series, exhibit strong long-range correlation. For substrings with length K=8, the $D_{q}$ spectra of all organisms studied are multifractal-like and sufficiently smooth for the $C_{q}$ curves to be meaningful. The $C_{q}$ curves of all bacteria resemble a classical phase transition at a critical point. But the 'analogous' phase transitions of chromosomes of non-bacteria organisms are different. Apart from Chromosome 1 of {\it C. elegans}, they exhibit the shape of double-peaked specific heat function.Comment: 12 pages with 9 figures and 1 tabl

Phylogenetic Tree Construction for Starfish and Primate Genomes via Alignment Free Methods

A phylogenetic tree is a tree like diagram showing the evolutionary relationship among various species based on their differences or similarity in their physical or genetic makeup.The similarity in their genetic makeup is traditionally measured based on pairwise distance between their gene sequences using sequence alignment methods. Due to the advancement in next generation sequencing technologies there is a huge amount of datasets available for partially or completely sequenced genomes. These massive datasets requires a faster comparison methods other than the traditional alignment-based approaches. Therefore, alignment free approaches are gaining popularity in recent years. In this thesis, we compare alignment-based and various alignment free methods for phylogenetic tree construction. The alignment free methods we study are based on k-mer frequency, Average Common Substring (ACS) and ACS with position restrictions and mismatches. The position restricted ACS is a novel contribution of this thesis. To evaluate performance of the alignment free approaches we applied it to phylogeny reconstruction using DNA ( 27 primate mitochondrial genomes) and protein (Starfish RNA-seq) sequence sets. The phylogenetic trees are constructed using Neighbor joining to the distance matrices obtained with the above mentioned alignment-free methods. The resulting phylogenetic trees are then compared with the reference tree using Branch Score Distance measure. Both the Neighbor joining and the Branch Score Distance Measure are calculated by using the programs neighbor and treedist from the PHYLIP package