Entropic Profiles, Maximal Motifs and the Discovery of Significant Repetitions in Genomic Sequences. In: Brown D, Morgenstern B, editors. Algorithms in Bioinformatics. Berlin: Springer Berlin Heidelberg; 2014. pp. 148-60. [DOI: 10.1007/978-3-662-44753-6_12]

Efficient Algorithms for Sequence Analysis with Entropic Profiles

Entropy, being closely related to repetitiveness and compressibility, is a widely used information-related measure to assess the degree of predictability of a sequence. Entropic profiles are based on information theory principles, and can be used to study the under-/over-representation of subwords, by also providing information about the scale of conserved DNA regions. Here, we focus on the algorithmic aspects related to entropic profiles. In particular, we propose linear time algorithms for their computation that rely on suffix-based data structures, more specifically on the truncated suffix tree (TST) and on the enhanced suffix array (ESA). We performed an extensive experimental campaign showing that our algorithms, beside being faster, make it possible the analysis of longer sequences, even for high degrees of resolution, than state of the art algorithms.

On the comparison of regulatory sequences with multiple resolution Entropic Profiles

Background

Enhancers are stretches of DNA (100–1000 bp) that play a major role in development gene expression, evolution and disease. It has been recently shown that in high-level eukaryotes enhancers rarely work alone, instead they collaborate by forming clusters of cis-regulatory modules (CRMs). Although the binding of transcription factors is sequence-specific, the identification of functionally similar enhancers is very difficult and it cannot be carried out with traditional alignment-based techniques.

Results

The use of fast similarity measures, like alignment-free measures, to detect related regulatory sequences is crucial to understand functional correlation between two enhancers. In this paper we study the use of alignment-free measures for the classification of CRMs. However, alignment-free measures are generally tied to a fixed resolution k. Here we propose an alignment-free statistic, called \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$EP^{*}_{2}$\end{document}EP2∗, that is based on multiple resolution patterns derived from the Entropic Profiles (EPs). The Entropic Profile is a function of the genomic location that captures the importance of that region with respect to the whole genome. As a byproduct we provide a formula to compute the exact variance of variable length word counts, a result that can be of general interest also in other applications.

Conclusions

We evaluate several alignment-free statistics on simulated data and real mouse ChIP-seq sequences. The new statistic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$EP^{*}_{2}$\end{document}EP2∗, is highly successful in discriminating functionally related enhancers and, in almost all experiments, it outperforms fixed-resolution methods. We implemented the new alignment-free measures, as well as traditional ones, in a software called EP-sim that is freely available: http://www.dei.unipd.it/~ciompin/main/EP-sim.html.