Alignment-free Sequence Comparison Research Articles

Numerical characterization of DNA sequences: connectivity type indices derived from DNA line graphs

The four-letter code sequence of a single strand of a DNA sequence was converted into a line graph, and the vertices of the line graph were assigned weights according to the dissociation constant (pKa) of the corresponding nitrogenous base represented by each of the vertices. Connectivity type indices were computed for the weighted line graphs and the numerical descriptors thus calculated were used for alignment-free sequence comparison. The numerical descriptors proposed in this study were calculated very fast even for whole genomes, and thus, the methodology enabled alignment-free comparison of long DNA sequences without much computational load. Sequence comparison using numerical descriptors derived from the weighted line graphs is illustrated using 23 mitochondrial genomic sequences. The cladogram obtained from the hierarchical clustering carried out using the numerical descriptors grouped evolutionarily similar sequences together.

Statistical considerations underpinning an alignment-free sequence comparison method

The D 2 statistic is defined as the number of word matches of prespecified length k , with up to t mismatches, shared between two given sequences. This statistic finds its application in alignment-free comparisons of biological sequences. It has two main advantages over alignment-based methods for nucleotide and amino-acid sequence comparisons, such as BLAST (basic local alignment search tool). These are (i) D 2 does not assume that homologous segments are contiguous, and (ii) the algorithm is computationally extremely fast, the runtime being proportional to the size of the sequences in the case of exact matches. This review article summarises results to date on determining the distributional properties of the D 2 statistic for a range of biologically relevant parameters, describes existing applications of the method, and outlines future research directions.

Alignment-Free Sequence Comparison (I): Statistics and Power

Large-scale comparison of the similarities between two biological sequences is a major issue in computational biology; a fast method, the D(2) statistic, relies on the comparison of the k-tuple content for both sequences. Although it has been known for some years that the D(2) statistic is not suitable for this task, as it tends to be dominated by single-sequence noise, to date no suitable adjustments have been proposed. In this article, we suggest two new variants of the D(2) word count statistic, which we call D(2)(S) and D(2)(*). For D(2)(S), which is a self-standardized statistic, we show that the statistic is asymptotically normally distributed, when sequence lengths tend to infinity, and not dominated by the noise in the individual sequences. The second statistic, D(2)(*), outperforms D(2)(S) in terms of power for detecting the relatedness between the two sequences in our examples; but although it is straightforward to simulate from the asymptotic distribution of D(2)(*), we cannot provide a closed form for power calculations.

Empirical distribution of k-word matches in biological sequences

This study focuses on an alignment-free sequence comparison method: the number of words of length k shared between two sequences, also known as the D 2 statistic. The advantages of the use of this statistic over alignment-based methods are firstly that it does not assume that homologous segments are contiguous, and secondly that the algorithm is computationally extremely fast, the runtime being proportional to the size of the sequence under scrutiny. Existing applications of the D 2 statistic include the clustering of related sequences in large EST databases such as the STACK database. Such applications have typically relied on heuristics without any statistical basis. Rigorous statistical characterisations of the distribution of D 2 have subsequently been undertaken, but have focussed on the distribution's asymptotic behaviour, leaving the distribution of D 2 uncharacterised for most practical cases. The work presented here bridges these two worlds to give usable approximations of the distribution of D 2 for ranges of parameters most frequently encountered in the study of biological sequences.

A statistical method for alignment-free comparison of regulatory sequences

The similarity of two biological sequences has traditionally been assessed within the well-established framework of alignment. Here we focus on the task of identifying functional relationships between cis-regulatory sequences that are non-orthologous or greatly diverged. 'Alignment-free' measures of sequence similarity are required in this regime. We investigate the use of a new score for alignment-free sequence comparison, called the score. It is based on comparing the frequencies of all fixed-length words in the two sequences. An important, novel feature of the score is that it is comparable across sequence pairs drawn from arbitrary background distributions. We present a method that gives quadratic improvement in the time complexity of calculating the score, over the naïve method. We then evaluate the score on several tissue-specific families of cis-regulatory modules (in Drosophila and human). The new score is highly successful in discriminating functionally related regulatory sequences from unrelated sequence pairs. The performance of the score is compared to five other alignment-free similarity measures, and shown to be consistently superior to all of these measures. Our implementation of the score will be made freely available as source code, upon publication of this article, at: http://veda.cs.uiuc.edu/d2z/. Supplementary data are available at Bioinformatics online.