Simplifying the mosaic description of DNA sequences

Abstract

By using the Jensen-Shannon divergence, genomic DNA can be divided into compositionally distinct domains through a standard recursive segmentation procedure. Each domain, while significantly different from its neighbours, may however share compositional similarity with one or more distant (nonneighbouring) domains. We thus obtain a coarse-grained description of the given DNA string in terms of a smaller set of distinct domain labels. This yields a minimal domain description of a given DNA sequence, significantly reducing its organizational complexity. This procedure gives a new means of evaluating genomic complexity as one examines organisms ranging from bacteria to human. The mosaic organization of DNA sequences could have originated from the insertion of fragments of one genome (the parasite) inside another (the host), and we present numerical experiments that are suggestive of this scenario.

Segmentation and dimensionality reduction

“…Guha et al [10] provide a graceful tradeoff between the running time and the quality of the obtained solution. Azad et al [2], Li [16], and Ramensky et al [20] apply segmentation on genomic sequences, while Koivisto et al [15] use segmentation to find blocks on haplotypes. One should note that in statistics the question of segmentation of a sequence or time series is often called the change-point problem [6].…”

“…In order to reduce the dimensionality from d to m we perform PCA on the set of weighted points U S . 2 The PCA computation gives for each segment vector u j an approximate representation u j such that…”

Finding recurrent sources in sequences

“…In his formulation he uses hidden Markov states to model different compositional properties within each DNA segment, and his solution uses the Viterbi algorithm to determine the most probable sequence of states. More recently, Azad et al [2] formulate a similar problem to (k, h)-segmentation but their solution is based on greedy "split and merge" and it does not provide any theoretical guarantee.…”

“…The segmentation problem for genome sequences and time series has been discussed widely; see, e.g., [10,3,7,9,5,16,14,15,11,4,2]. For a wide variety of score functions, dynamic programming can be used to obtain the best segmentation of an n-element sequence into k pieces in time O(n 2 k); this idea goes back at least to Bellman [3] in 1961.…”

“…For instance, Azad et al [2] try to identify a coarsegrained description of the given DNA string in terms of a smaller set of distinct domain labels. The biological hypothesis behind this is that a mosaic organization of DNA sequences could have originated from the insertion of fragments of one genome (the parasite) inside another (the host).…”