Computing distribution of scale independent motifs in biological sequences

Alignment-Free Sequence Comparison: A Systematic Survey From a Machine Learning Perspective

The encounter of large amounts of biological sequence data generated during the last decades and the algorithmic and hardware improvements have offered the possibility to apply machine learning techniques in bioinformatics. While the machine learning community is aware of the necessity to rigorously distinguish data transformation from data comparison and adopt reasonable combinations thereof, this awareness is often lacking in the field of comparative sequence analysis. With realization of the disadvantages of alignments for sequence comparison, some typical applications use more and more so-called alignment-free approaches. In light of this development, we present a conceptual framework for alignment-free sequence comparison, which highlights the delineation of: 1) the sequence data transformation comprising of adequate mathematical sequence coding and feature generation, from 2) the subsequent (dis-)similarity evaluation of the transformed data by means of problem-specific but mathematically consistent proximity measures. We consider coding to be an information-loss free data transformation in order to get an appropriate representation, whereas feature generation is inevitably information-lossy with the intention to extract just the task-relevant information. This distinction sheds light on the plethora of methods available and assists in identifying suitable methods in machine learning and data analysis to compare the sequences under these premises.

Additive methods for genomic signatures

Background

Studies exploring the potential of Chaos Game Representations (CGR) of genomic sequences to act as “genomic signatures” (to be species- and genome-specific) showed that CGR patterns of nuclear and organellar DNA sequences of the same organism can be very different. While the hypothesis that CGRs of mitochondrial DNA sequences can act as genomic signatures was validated for a snapshot of all sequenced mitochondrial genomes available in the NCBI GenBank sequence database, to our knowledge no such extensive analysis of CGRs of nuclear DNA sequences exists to date.

Results

We analyzed an extensive dataset, totalling 1.45 gigabase pairs, of nuclear/nucleoid genomic sequences (nDNA) from 42 different organisms, spanning all major kingdoms of life. Our computational experiments indicate that CGR signatures of nDNA of two different origins cannot always be differentiated, especially if they originate from closely-related species such as H. sapiens and P. troglodytes or E. coli and E. fergusonii. To address this issue, we propose the general concept of additive DNA signature of a set (collection) of DNA sequences. One particular instance, the composite DNA signature, combines information from nDNA fragments and organellar (mitochondrial, chloroplast, or plasmid) genomes. We demonstrate that, in this dataset, composite DNA signatures originating from two different organisms can be differentiated in all cases, including those where the use of CGR signatures of nDNA failed or was inconclusive. Another instance, the assembled DNA signature, combines information from many short DNA subfragments (e.g., 100 basepairs) of a given DNA fragment, to produce its signature. We show that an assembled DNA signature has the same distinguishing power as a conventionally computed CGR signature, while using shorter contiguous sequences and potentially less sequence information.

Conclusions

Our results suggest that, while CGR signatures of nDNA cannot always play the role of genomic signatures, composite and assembled DNA signatures (separately or in combination) could potentially be used instead. Such additive signatures could be used, e.g., with raw unassembled next-generation sequencing (NGS) read data, when high-quality sequencing data is not available, or to complement information obtained by other methods of species identification or classification.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1157-8) contains supplementary material, which is available to authorized users.

An investigation into inter- and intragenomic variations of graphic genomic signatures

Background

Motivated by the general need to identify and classify species based on molecular evidence, genome comparisons have been proposed that are based on measuring mostly Euclidean distances between Chaos Game Representation (CGR) patterns of genomic DNA sequences.

Results

We provide, on an extensive dataset and using several different distances, confirmation of the hypothesis that CGR patterns are preserved along a genomic DNA sequence, and are different for DNA sequences originating from genomes of different species. This finding lends support to the theory that CGRs of genomic sequences can act as graphic genomic signatures. In particular, we compare the CGR patterns of over five hundred different 150,000 bp genomic sequences spanning one complete chromosome from each of six organisms, representing all kingdoms of life: H. sapiens (Animalia; chromosome 21), S. cerevisiae (Fungi; chromosome 4), A. thaliana (Plantae; chromosome 1), P. falciparum (Protista; chromosome 14), E. coli (Bacteria - full genome), and P. furiosus (Archaea - full genome). To maximize the diversity within each species, we also analyze the interrelationships within a set of over five hundred 150,000 bp genomic sequences sampled from the entire aforementioned genomes. Lastly, we provide some preliminary evidence of this method’s ability to classify genomic DNA sequences at lower taxonomic levels by comparing sequences sampled from the entire genome of H. sapiens (class Mammalia, order Primates) and of M. musculus (class Mammalia, order Rodentia), for a total length of approximately 174 million basepairs analyzed. We compute pairwise distances between CGRs of these genomic sequences using six different distances, and construct Molecular Distance Maps, which visualize all sequences as points in a two-dimensional or three-dimensional space, to simultaneously display their interrelationships.

Conclusion

Our analysis confirms, for this dataset, that CGR patterns of DNA sequences from the same genome are in general quantitatively similar, while being different for DNA sequences from genomes of different species. Our assessment of the performance of the six distances analyzed uses three different quality measures and suggests that several distances outperform the Euclidean distance, which has so far been almost exclusively used for such studies.

Information theory applications for biological sequence analysis

Information theory (IT) addresses the analysis of communication systems and has been widely applied in molecular biology. In particular, alignment-free sequence analysis and comparison greatly benefited from concepts derived from IT, such as entropy and mutual information. This review covers several aspects of IT applications, ranging from genome global analysis and comparison, including block-entropy estimation and resolution-free metrics based on iterative maps, to local analysis, comprising the classification of motifs, prediction of transcription factor binding sites and sequence characterization based on linguistic complexity and entropic profiles. IT has also been applied to high-level correlations that combine DNA, RNA or protein features with sequence-independent properties, such as gene mapping and phenotype analysis, and has also provided models based on communication systems theory to describe information transmission channels at the cell level and also during evolutionary processes. While not exhaustive, this review attempts to categorize existing methods and to indicate their relation with broader transversal topics such as genomic signatures, data compression and complexity, time series analysis and phylogenetic classification, providing a resource for future developments in this promising area.

Sequence analysis by iterated maps, a review

Among alignment-free methods, Iterated Maps (IMs) are on a particular extreme: they are also scale free (order free). The use of IMs for sequence analysis is also distinct from other alignment-free methodologies in being rooted in statistical mechanics instead of computational linguistics. Both of these roots go back over two decades to the use of fractal geometry in the characterization of phase-space representations. The time series analysis origin of the field is betrayed by the title of the manuscript that started this alignment-free subdomain in 1990, 'Chaos Game Representation'. The clash between the analysis of sequences as continuous series and the better established use of Markovian approaches to discrete series was almost immediate, with a defining critique published in same journal 2 years later. The rest of that decade would go by before the scale-free nature of the IM space was uncovered. The ensuing decade saw this scalability generalized for non-genomic alphabets as well as an interest in its use for graphic representation of biological sequences. Finally, in the past couple of years, in step with the emergence of BigData and MapReduce as a new computational paradigm, there is a surprising third act in the IM story. Multiple reports have described gains in computational efficiency of multiple orders of magnitude over more conventional sequence analysis methodologies. The stage appears to be now set for a recasting of IMs with a central role in processing nextgen sequencing results.

Fractal MapReduce decomposition of sequence alignment

BACKGROUND

The dramatic fall in the cost of genomic sequencing, and the increasing convenience of distributed cloud computing resources, positions the MapReduce coding pattern as a cornerstone of scalable bioinformatics algorithm development. In some cases an algorithm will find a natural distribution via use of map functions to process vectorized components, followed by a reduce of aggregate intermediate results. However, for some data analysis procedures such as sequence analysis, a more fundamental reformulation may be required.

RESULTS

In this report we describe a solution to sequence comparison that can be thoroughly decomposed into multiple rounds of map and reduce operations. The route taken makes use of iterated maps, a fractal analysis technique, that has been found to provide a "alignment-free" solution to sequence analysis and comparison. That is, a solution that does not require dynamic programming, relying on a numeric Chaos Game Representation (CGR) data structure. This claim is demonstrated in this report by calculating the length of the longest similar segment by inspecting only the USM coordinates of two analogous units: with no resort to dynamic programming.

CONCLUSIONS

The procedure described is an attempt at extreme decomposition and parallelization of sequence alignment in anticipation of a volume of genomic sequence data that cannot be met by current algorithmic frameworks. The solution found is delivered with a browser-based application (webApp), highlighting the browser's emergence as an environment for high performance distributed computing.

AVAILABILITY

Public distribution of accompanying software library with open source and version control at http://usm.github.com. Also available as a webApp through Google Chrome's WebStore http://chrome.google.com/webstore: search with "usm".

Pattern matching through Chaos Game Representation: bridging numerical and discrete data structures for biological sequence analysis

Background

Chaos Game Representation (CGR) is an iterated function that bijectively maps discrete sequences into a continuous domain. As a result, discrete sequences can be object of statistical and topological analyses otherwise reserved to numerical systems. Characteristically, CGR coordinates of substrings sharing an L-long suffix will be located within 2^-L distance of each other. In the two decades since its original proposal, CGR has been generalized beyond its original focus on genomic sequences and has been successfully applied to a wide range of problems in bioinformatics. This report explores the possibility that it can be further extended to approach algorithms that rely on discrete, graph-based representations.

Results

The exploratory analysis described here consisted of selecting foundational string problems and refactoring them using CGR-based algorithms. We found that CGR can take the role of suffix trees and emulate sophisticated string algorithms, efficiently solving exact and approximate string matching problems such as finding all palindromes and tandem repeats, and matching with mismatches. The common feature of these problems is that they use longest common extension (LCE) queries as subtasks of their procedures, which we show to have a constant time solution with CGR. Additionally, we show that CGR can be used as a rolling hash function within the Rabin-Karp algorithm.

Conclusions

The analysis of biological sequences relies on algorithmic foundations facing mounting challenges, both logistic (performance) and analytical (lack of unifying mathematical framework). CGR is found to provide the latter and to promise the former: graph-based data structures for sequence analysis operations are entailed by numerical-based data structures produced by CGR maps, providing a unifying analytical framework for a diversity of pattern matching problems.

New method for comparing DNA primary sequences based on a discrimination measure

We introduce a new approach to compare DNA primary sequences. The core of our method is a new measure of pairwise distances among sequences. Using the primitive discrimination substrings of sequence S and Q, a discrimination measure DM(S, Q) is defined for the similarity analysis of them. The proposed method does not require multiple alignments and is fully automatic. To illustrate its utility, we construct phylogenetic trees on two independent data sets. The results indicate that the method is efficient and powerful.

A web server for interactive and zoomable Chaos Game Representation images

Chaos Game Representation (CGR) is a generalized scale-independent Markov transition table, which is useful for the visualization and comparative study of genomic signature, or for the study of characteristic sequence motifs. However, in order to fully utilize the scale-independent properties of CGR, it should be accessible through scale-independent user interface instead of static images. Here we describe a web server and Perl library for generating zoomable CGR images utilizing Google Maps API, which is also easily searchable for specific motifs. The web server is freely accessible at http://www.g-language.org/wiki/cgr/, and the Perl library as well as the source code is distributed with the G-language Genome Analysis Environment under GNU General Public License.

Biological sequences as pictures: a generic two dimensional solution for iterated maps

BACKGROUND

Representing symbolic sequences graphically using iterated maps has enjoyed an enduring popularity since it was first proposed in Jeffrey 1990 as chaos game representation (CGR). The usefulness of this representation goes beyond the convenience of a scale independent representation. It provides a variable memory length representation of transition. This includes the representation of succession with non-integer order, which comes with the promise of generalizing Markovian formalisms. The original proposal targeted genomic sequences only but since then several generalizations have been proposed, many specifically designed to handle protein data.

RESULTS

The challenge of a general solution is that of deriving a bijective transformation of symbolic sequences into bi-dimensional planes. More specifically, it requires the regular fractal nesting of polygons. A first attempt at a general solution was proposed by Fiser 1994 by using non-overlapping circles that contain the polygons. This was used as a starting point to identify a more efficient solution where the encapsulating circles can overlap without the same happening for the sequence maps which are circumscribed to fractal polygon domains.

CONCLUSION

We identified the optimal inscribed packing solution for iterated maps of any Biological sequence, indeed of any symbolic sequence. The new solution maintains the prized bijective mapping property and includes the Sierpinski triangle and the CGR square as particular solutions of the more encompassing formulation.

Exploring an alignment free approach for protein classification and structural class prediction

Alignment free methods based on Chaos Game Representation (CGR), also known as sequence signature approaches, have proven of great interest for DNA sequence analysis. Indeed, they have been successfully applied for sequence comparison, phylogeny, detection of horizontal transfers or extraction of representative motifs in regulation sequences. Transposing such methods to proteins poses several fundamental questions related to representation space dimensionality. Several studies have tackled these points, but none has, so far, brought the application of CGRs to proteins to their fully expected potential. Yet, several studies have shown that techniques based on n-peptide frequencies can be relevant for proteins. Here, we investigate the effectiveness of a strategy based on the CGR approach using a fixed reverse encoding of amino acids into nucleic sequences. We first explore its relevance to protein classification into functional families. We then attempt to apply it to the prediction of protein structural classes. Our results suggest that the reverse encoding approach could be relevant in both cases. We show that it is able to classify functional families of proteins by extracting signatures close to the ProSite patterns. Applied to structural classification, the approach reaches scores of correct classification close to 84%, i.e. close to the scores of related methods in the field. Various optimizations of the approach are still possible, which open the door for future applications.

Local Renyi entropic profiles of DNA sequences

Background

In a recent report the authors presented a new measure of continuous entropy for DNA sequences, which allows the estimation of their randomness level. The definition therein explored was based on the Rényi entropy of probability density estimation (pdf) using the Parzen's window method and applied to Chaos Game Representation/Universal Sequence Maps (CGR/USM). Subsequent work proposed a fractal pdf kernel as a more exact solution for the iterated map representation. This report extends the concepts of continuous entropy by defining DNA sequence entropic profiles using the new pdf estimations to refine the density estimation of motifs.

Results

The new methodology enables two results. On the one hand it shows that the entropic profiles are directly related with the statistical significance of motifs, allowing the study of under and over-representation of segments. On the other hand, by spanning the parameters of the kernel function it is possible to extract important information about the scale of each conserved DNA region. The computational applications, developed in Matlab m-code, the corresponding binary executables and additional material and examples are made publicly available at .

Conclusion

The ability to detect local conservation from a scale-independent representation of symbolic sequences is particularly relevant for biological applications where conserved motifs occur in multiple, overlapping scales, with significant future applications in the recognition of foreign genomic material and inference of motif structures.