Empirical distribution of k-word matches in biological sequences

TL;DR

This paper provides practical statistical approximations for the distribution of the D_2 statistic, an alignment-free method for comparing biological sequences based on shared k-word counts, enhancing its application in sequence analysis.

Contribution

It offers the first usable approximations of D_2's distribution for common biological sequence parameters, bridging theoretical and practical needs.

Findings

Provides statistical models for D_2 distribution in biological sequences

Enables more accurate significance testing in sequence comparison

Improves the reliability of clustering in large sequence databases

Abstract

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.