Quaternionic periodicity transform: an algebraic solution to the tandem repeat detection problem

Detection of Tandem Repeats in DNA Sequences Using Short-Time Ramanujan Fourier Transform

Tandem repeats in genomic sequences are characterized by two or more contiguous copies of a pattern of nucleotides. The role of these repeats as molecular markers is well established in various genetic disorders, human evolution studies, DNA forensics and intron retention. In this work a computational method has been developed for the extraction of both exact and approximate tandem repeats. The proposed algorithm uses Ramanujan Fourier Transform (RFT) to identify periodicities in the DNA sequences. Since RFT estimates the period directly, rather than inferring it from the signal's spectrum, it provides a more sensitive and rapid detection of tandem repeats as compared to other available popular computational methods.

Finding long tandem repeats in long noisy reads

Motivation

Long tandem repeat expansions of more than 1000 nt have been suggested to be associated with diseases, but remain largely unexplored in individual human genomes because read lengths have been too short. However, new long-read sequencing technologies can produce single reads of 10 000 nt or more that can span such repeat expansions, although these long reads have high error rates, of 10–20%, which complicates the detection of repetitive elements. Moreover, most traditional algorithms for finding tandem repeats are designed to find short tandem repeats (<1000 nt) and cannot effectively handle the high error rate of long reads in a reasonable amount of time.

Results

Here, we report an efficient algorithm for solving this problem that takes advantage of the length of the repeat. Namely, a long tandem repeat has hundreds or thousands of approximate copies of the repeated unit, so despite the error rate, many short k-mers will be error-free in many copies of the unit. We exploited this characteristic to develop a method for first estimating regions that could contain a tandem repeat, by analyzing the k-mer frequency distributions of fixed-size windows across the target read, followed by an algorithm that assembles the k-mers of a putative region into the consensus repeat unit by greedily traversing a de Bruijn graph. Experimental results indicated that the proposed algorithm largely outperformed Tandem Repeats Finder, a widely used program for finding tandem repeats, in terms of sensitivity.

Availability and implementation

https://github.com/morisUtokyo/mTR.

Tandem repeats detection in DNA sequences using Kaiser window based adaptive S-transform

In computational biology the development of algorithms for the identification of tandem repeats in DNA sequences is a challenging problem. Tandem repeats identification is helpful in gene annotation, forensics, and the study of human evolution. In this work a signal processing algorithm based on adaptive S-transform, with Kaiser window, has been proposed for the exact and approximate tandem repeats detection. Usage of Kaiser window helped in identifying short as well as long tandem repeats. Thus, the limitation of earlier S-transform based algorithm that identified only microsatellites has been alleviated by this more versatile algorithm. The superiority of this algorithm has been established by comparative simulation studies with other reported methods.

Searching microsatellites in DNA sequences: approaches used and tools developed

Microsatellite instability associated genomic activities and evolutionary changes have led to a renewed focus on microsatellite research. In last decade, a number of microsatellite mining tools have been introduced based on different computational approaches. The choice is generally made between slow but exhaustive dynamic programming based approaches, or fast and incomplete heuristic methods. Tools based on stochastic approaches are more popular due to their simplicity and added ornamental features. We have performed a comparative evaluation of the relative efficiency of some microsatellite search tools with their default settings. The graphical user interface, the statistical analysis of the output and ability to mine imperfect repeats are the most important criteria in selecting a tool for a particular investigation. However, none of the available tools alone provides complete and accurate information about microsatellites, and a lot depends on the discretion of the user.

Origin of multiple periodicities in the Fourier power spectra of the Plasmodium falciparum genome

Background

Fourier transforms and their associated power spectra are used for detecting periodicities and protein-coding genes and is generally regarded as a well established technique. Many of the periodicities which have been found with this method are quite well understood such as the periodicity of 3 nt which is associated to codon usage. But what is the origin of the peculiar frequency multiples k/21 which were reported for a tiny section of chromosome 2 in P. falciparum? Are these present in other chromosomes and perhaps in related organisms? And how should we interpret fractional periodicities in genomes?

Results

We applied the binary indicator power spectrum to all chromosomes of P. falciparum, and found that the frequency overtones k/21 are present only in non-coding sections. We did not find such frequency overtones in any other related genomes. Furthermore, the frequency overtones were identified as artifacts of the way the genome is encoded into a numerical sequence, that is, they are frequency aliases. By choosing a different way to encode the sequence the overtones do not appear. In view of these results, we revisited early applications of this technique to proteins where frequency overtones were reported.

Conclusions

Some authors hinted recently at the possibility of mapping artifacts and frequency aliases in power spectra. However, in the case of P. falciparum the frequency aliases are particularly strong and can mask the 1/3 frequency which is used for gene detecting. This shows that albeit being a well known technique, with a long history of application in proteins, few researchers seem to be aware of the problems represented by frequency aliases.

A new approach to in silico SNP detection and some new SNPs in the Bacillus anthracis genome

Background

Bacillus anthracis is one of the most monomorphic pathogens known. Identification of polymorphisms in its genome is essential for taxonomic classification, for determination of recent evolutionary changes, and for evaluation of pathogenic potency.

Findings

In this work three strains of the Bacillus anthracis genome are compared and previously unpublished single nucleotide polymorphisms (SNPs) are revealed. Moreover, it is shown that, despite the highly monomorphic nature of Bacillus anthracis, the SNPs are (1) abundant in the genome and (2) distributed relatively uniformly across the sequence.

Conclusions

The findings support the proposition that SNPs, together with indels and variable number tandem repeats (VNTRs), can be used effectively not only for the differentiation of perfect strain data, but also for the comparison of moderately incomplete, noisy and, in some cases, unknown Bacillus anthracis strains. In the case when the data is of still lower quality, a new DNA sequence fingerprinting approach based on recently introduced markers, based on combinatorial-analytic concepts and called cyclic difference sets, can be used.

TRStalker: an efficient heuristic for finding fuzzy tandem repeats

Motivation: Genomes in higher eukaryotic organisms contain a substantial amount of repeated sequences. Tandem Repeats (TRs) constitute a large class of repetitive sequences that are originated via phenomena such as replication slippage and are characterized by close spatial contiguity. They play an important role in several molecular regulatory mechanisms, and also in several diseases (e.g. in the group of trinucleotide repeat disorders). While for TRs with a low or medium level of divergence the current methods are rather effective, the problem of detecting TRs with higher divergence (fuzzy TRs) is still open. The detection of fuzzy TRs is propaedeutic to enriching our view of their role in regulatory mechanisms and diseases. Fuzzy TRs are also important as tools to shed light on the evolutionary history of the genome, where higher divergence correlates with more remote duplication events.

Results: We have developed an algorithm (christened TRStalker) with the aim of detecting efficiently TRs that are hard to detect because of their inherent fuzziness, due to high levels of base substitutions, insertions and deletions. To attain this goal, we developed heuristics to solve a Steiner version of the problem for which the fuzziness is measured with respect to a motif string not necessarily present in the input string. This problem is akin to the ‘generalized median string’ that is known to be an NP-hard problem. Experiments with both synthetic and biological sequences demonstrate that our method performs better than current state of the art for fuzzy TRs and that the fuzzy TRs of the type we detect are indeed present in important biological sequences.

Availability: TRStalker will be integrated in the web-based TRs Discovery Service (TReaDS) at bioalgo.iit.cnr.it.

Contact:marco.pellegrini@iit.cnr.it

Supplementary information:Supplementary data are available at Bioinformatics online.

Hierarchical structure of cascade of primary and secondary periodicities in Fourier power spectrum of alphoid higher order repeats

Background

Identification of approximate tandem repeats is an important task of broad significance and still remains a challenging problem of computational genomics. Often there is no single best approach to periodicity detection and a combination of different methods may improve the prediction accuracy. Discrete Fourier transform (DFT) has been extensively used to study primary periodicities in DNA sequences. Here we investigate the application of DFT method to identify and study alphoid higher order repeats.

Results

We used method based on DFT with mapping of symbolic into numerical sequence to identify and study alphoid higher order repeats (HOR). For HORs the power spectrum shows equidistant frequency pattern, with characteristic two-level hierarchical organization as signature of HOR. Our case study was the 16 mer HOR tandem in AC017075.8 from human chromosome 7. Very long array of equidistant peaks at multiple frequencies (more than a thousand higher harmonics) is based on fundamental frequency of 16 mer HOR. Pronounced subset of equidistant peaks is based on multiples of the fundamental HOR frequency (multiplication factor n for nmer) and higher harmonics. In general, nmer HOR-pattern contains equidistant secondary periodicity peaks, having a pronounced subset of equidistant primary periodicity peaks. This hierarchical pattern as signature for HOR detection is robust with respect to monomer insertions and deletions, random sequence insertions etc. For a monomeric alphoid sequence only primary periodicity peaks are present. The 1/f^β – noise and periodicity three pattern are missing from power spectra in alphoid regions, in accordance with expectations.

Conclusion

DFT provides a robust detection method for higher order periodicity. Easily recognizable HOR power spectrum is characterized by hierarchical two-level equidistant pattern: higher harmonics of the fundamental HOR-frequency (secondary periodicity) and a subset of pronounced peaks corresponding to constituent monomers (primary periodicity). The number of lower frequency peaks (secondary periodicity) below the frequency of the first primary periodicity peak reveals the size of nmer HOR, i.e., the number n of monomers contained in consensus HOR.