Abstract
BackgroundFinding new functional fragments in biological sequences is a challenging problem. Methods addressing this problem commonly search for clusters of pattern occurrences that are statistically significant. A measure of statistical significance is the P-value of a number of pattern occurrences, i.e. the probability to find at least S occurrences of words from a pattern in a random text of length N generated according to a given probability model. All words of the pattern are supposed to be of same length.ResultsWe present a novel algorithm SufPref that computes an exact P-value for Hidden Markov models (HMM). The algorithm is based on recursive equations on text sets related to pattern occurrences; the equations can be used for any probability model. The algorithm inductively traverses a specific data structure, an overlap graph. The nodes of the graph are associated with the overlaps of words from . The edges are associated to the prefix and suffix relations between overlaps. An originality of our data structure is that pattern need not be explicitly represented in nodes or leaves. The algorithm relies on the Cartesian product of the overlap graph and the graph of HMM states; this approach is analogous to the automaton approach from JBCB 4: 553-569. The gain in size of SufPref data structure leads to significant improvements in space and time complexity compared to existent algorithms. The algorithm SufPref was implemented as a C++ program; the program can be used both as Web-server and a stand alone program for Linux and Windows. The program interface admits special formats to describe probability models of various types (HMM, Bernoulli, Markov); a pattern can be described with a list of words, a PSSM, a degenerate pattern or a word and a number of mismatches. It is available at http://server2.lpm.org.ru/bio/online/sf/. The program was applied to compare sensitivity and specificity of methods for TFBS prediction based on P-values computed for Bernoulli models, Markov models of orders one and two and HMMs. The experiments show that the methods have approximately the same qualities.Electronic supplementary materialThe online version of this article (doi:10.1186/s13015-014-0025-1) contains supplementary material, which is available to authorized users.
Highlights
Finding new functional fragments in biological sequences is a challenging problem
Hidden Markov models (HMM) were considered in only a few papers [5,6] despite the models being widely used in bioinformatics
This work presents an approach to compute the P-value of multiple pattern occurrence within a randomly generated text of a given length
Summary
Finding new functional fragments in biological sequences is a challenging problem Methods addressing this problem commonly search for clusters of pattern occurrences that are statistically significant. Many functionally significant fragments are characterized by a set of specific words that is called a pattern and denoted H below. Hidden Markov models (HMM) were considered in only a few papers [5,6] despite the models being widely used in bioinformatics. This is a motivation to develop methods for P-value calculation with respect to HMMs
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