A measure of DNA sequence similarity by Fourier Transform with applications on hierarchical clustering

Use of 3D chaos game representation to quantify DNA sequence similarity with applications for hierarchical clustering

A 3D chaos game is shown to be a useful way for encoding DNA sequences. Since matching subsequences in DNA converge in space in 3D chaos game encoding, a DNA sequence's 3D chaos game representation can be used to compare DNA sequences without prior alignment and without truncating or padding any of the sequences. Two proposed methods inspired by shape-similarity comparison techniques show that this form of encoding can perform as well as alignment-based techniques for building phylogenetic trees. The first method uses the volume overlap of intersecting spheres and the second uses shape signatures by summarizing the coordinates, oriented angles, and oriented distances of the 3D chaos game trajectory. The methods are tested using: (1) the first exon of the beta-globin gene for 11 species, (2) mitochondrial DNA from four groups of primates, and (3) a set of synthetic DNA sequences. Simulations show that the proposed methods produce distances that reflect the number of mutation events; additionally, on average, distances resulting from deletion mutations are comparable to those produced by substitution mutations.

Positional difference and Frequency (PdF) based alignment-free technique for genome sequence comparison

In the field of computational biology, genome sequence comparison among different species is essential and has applications in both the research and scientific fields. Owing to the lengthy processing time and large number of data sets, the alignment-based approaches are unsuitable and ineffective. Therefore, alignment-free techniques have obtained popularity for acquiring proper sequence clustering and evolutionary relationship among species. In this paper, a complete bipartite graph based Positional difference and Frequency (PdF) vector descriptor is introduced. Positional difference and Frequency, two parameters, are applied to the genome sequence to create a 16- dimensional vector descriptor using the di-nucleotide representation of genome sequence. Subsequently, a distance matrix is calculated to construct the phylogenetic trees for different data sets of mammals and viruses. The achieved outcomes are compared with the phylogenetic trees of the earlier methods viz. the FFP method, the ClustalW method, the MEV method, the PCNV method and the FIS method. In most instances, the proposed method produces more precise outcomes than the preceding techniques and has potential for genome sequence comparison on both the equal and unequal length of data-sets.Communicated by Ramaswamy H. Sarma.

Predicting chromosomal compartments directly from the nucleotide sequence with DNA-DDA

Three-dimensional (3D) genome architecture is characterized by multi-scale patterns and plays an essential role in gene regulation. Chromatin conformation capturing experiments have revealed many properties underlying 3D genome architecture, such as the compartmentalization of chromatin based on transcriptional states. However, they are complex, costly and time consuming, and therefore only a limited number of cell types have been examined using these techniques. Increasing effort is being directed towards deriving computational methods that can predict chromatin conformation and associated structures. Here we present DNA-delay differential analysis (DDA), a purely sequence-based method based on chaos theory to predict genome-wide A and B compartments. We show that DNA-DDA models derived from a 20 Mb sequence are sufficient to predict genome wide compartmentalization at the scale of 100 kb in four different cell types. Although this is a proof-of-concept study, our method shows promise in elucidating the mechanisms responsible for genome folding as well as modeling the impact of genetic variation on 3D genome architecture and the processes regulated thereby.

A new gene tree algorithm employing DNA sequences of bovine genome using discrete Fourier transformation

Within the realms of human thoughts on nature, Fourier analysis is considered as one of the greatest ideas currently put forwarded. The Fourier transform shows that any periodic function can be rewritten as the sum of sinusoidal functions. Having a Fourier transform view on real-world problems like the DNA sequence of genes, would make things intuitively simple to understand in comparison with their initial formal domain view. In this study we used discrete Fourier transform (DFT) on DNA sequences of a set of genes in the bovine genome known to govern milk production, in order to develop a new gene clustering algorithm. The implementation of this algorithm is very user-friendly and requires only simple routine mathematical operations. By transforming the configuration of gene sequences into frequency domain, we sought to elucidate important features and reveal hidden gene properties. This is biologically appealing since no information is lost via this transformation and we are therefore not reducing the number of degrees of freedom. The results from different clustering methods were integrated using evidence accumulation algorithms to provide in insilico validation of our results. We propose using candidate gene sequences accompanied by other genes of biologically unknown function. These will then be assigned some degree of relevant annotation by using our proposed algorithm. Current knowledge in biological gene clustering investigation is also lacking, and so DFT-based methods will help shine a light on use of these algorithms for biological insight.

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.

A fast and efficient algorithm for DNA sequence similarity identification

DNA sequence similarity analysis is necessary for enormous purposes including genome analysis, extracting biological information, finding the evolutionary relationship of species. There are two types of sequence analysis which are alignment-based (AB) and alignment-free (AF). AB is effective for small homologous sequences but becomes NP-hard problem for long sequences. However, AF algorithms can solve the major limitations of AB. But most of the existing AF methods show high time complexity and memory consumption, less precision, and less performance on benchmark datasets. To minimize these limitations, we develop an AF algorithm using a 2D \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k-mer$$\end{document}k-mer count matrix inspired by the CGR approach. Then we shrink the matrix by analyzing the neighbors and then measure similarities using the best combinations of pairwise distance (PD) and phylogenetic tree methods. We also dynamically choose the value of k for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k-mer$$\end{document}k-mer. We develop an efficient system for finding the positions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k-mer$$\end{document}k-mer in the count matrix. We apply our system in six different datasets. We achieve the top rank for two benchmark datasets from AFproject, 100% accuracy for two datasets (16 S Ribosomal, 18 Eutherian), and achieve a milestone for time complexity and memory consumption in comparison to the existing study datasets (HEV, HIV-1). Therefore, the comparative results of the benchmark datasets and existing studies demonstrate that our method is highly effective, efficient, and accurate. Thus, our method can be used with the top level of authenticity for DNA sequence similarity measurement.

FFP: joint Fast Fourier transform and fractal dimension in amino acid property-aware phylogenetic analysis

Background

Amino acid property-aware phylogenetic analysis (APPA) refers to the phylogenetic analysis method based on amino acid property encoding, which is used for understanding and inferring evolutionary relationships between species from the molecular perspective. Fast Fourier transform (FFT) and Higuchi’s fractal dimension (HFD) have excellent performance in describing sequences’ structural and complexity information for APPA. However, with the exponential growth of protein sequence data, it is very important to develop a reliable APPA method for protein sequence analysis.

Results

Consequently, we propose a new method named FFP, it joints FFT and HFD. Firstly, FFP is used to encode protein sequences on the basis of the important physicochemical properties of amino acids, the dissociation constant, which determines acidity and basicity of protein molecules. Secondly, FFT and HFD are used to generate the feature vectors of encoded sequences, whereafter, the distance matrix is calculated from the cosine function, which describes the degree of similarity between species. The smaller the distance between them, the more similar they are. Finally, the phylogenetic tree is constructed. When FFP is tested for phylogenetic analysis on four groups of protein sequences, the results are obviously better than other comparisons, with the highest accuracy up to more than 97%.

Conclusion

FFP has higher accuracy in APPA and multi-sequence alignment. It also can measure the protein sequence similarity effectively. And it is hoped to play a role in APPA’s related research.

An efficient numerical representation of genome sequence: natural vector with covariance component

Background

The characterization and comparison of microbial sequences, including archaea, bacteria, viruses and fungi, are very important to understand their evolutionary origin and the population relationship. Most methods are limited by the sequence length and lack of generality. The purpose of this study is to propose a general characterization method, and to study the classification and phylogeny of the existing datasets.

Methods

We present a new alignment-free method to represent and compare biological sequences. By adding the covariance between each two nucleotides, the new 18-dimensional natural vector successfully describes 24,250 genomic sequences and 95,542 DNA barcode sequences. The new numerical representation is used to study the classification and phylogenetic relationship of microbial sequences.

Results

First, the classification results validate that the six-dimensional covariance vector is necessary to characterize sequences. Then, the 18-dimensional natural vector is further used to conduct the similarity relationship between giant virus and archaea, bacteria, other viruses. The nearest distance calculation results reflect that the giant viruses are closer to bacteria in distribution of four nucleotides. The phylogenetic relationships of the three representative families, Mimiviridae, Pandoraviridae and Marsellieviridae from giant viruses are analyzed. The trees show that ten sequences of Mimiviridae are clustered with Pandoraviridae, and Mimiviridae is closer to the root of the tree than Marsellieviridae. The new developed alignment-free method can be computed very fast, which provides an effective numerical representation for the sequence of microorganisms.

Use of DFT Distance Metrics for Classification of SARS-CoV-2 Genomes

In this work, we investigate using Fourier coefficients (FCs) for capturing useful information about viral sequences in a computationally efficient and compact manner. Specifically, we extract geographic submission location from SARS-CoV-2 sequence headers submitted to the GISAID Initiative, calculate corresponding FCs, and use the FCs to classify these sequences according to geographic location. We show that the FCs serve as useful numerical summaries for sequences that allow manipulation, identification, and differentiation via classical mathematical and statistical methods that are not readily applicable for character strings. Further, we argue that subsets of the FCs may be usable for the same purposes, which results in a reduction in storage requirements. We conclude by offering extensions of the research and potential future directions for subsequent analyses, such as the use of other series transforms for discreetly indexed signals such as genomes.

Full Chromosomal Relationships Between Populations and the Origin of Humans

A comprehensive description of human genomes is essential for understanding human evolution and relationships between modern populations. However, most published literature focuses on local alignment comparison of several genes rather than the complete evolutionary record of individual genomes. Combining with data from the 1,000 Genomes Project, we successfully reconstructed 2,504 individual genomes and propose Divided Natural Vector method to analyze the distribution of nucleotides in the genomes. Comparisons based on autosomes, sex chromosomes and mitochondrial genomes reveal the genetic relationships between populations, and different inheritance pattern leads to different phylogenetic results. Results based on mitochondrial genomes confirm the “out-of-Africa” hypothesis and assert that humans, at least females, most likely originated in eastern Africa. The reconstructed genomes are stored on our server and can be further used for any genome-scale analysis of humans (http://yaulab.math.tsinghua.edu.cn/2022_1000genomesprojectdata/). This project provides the complete genomes of thousands of individuals and lays the groundwork for genome-level analyses of the genetic relationships between populations and the origin of humans.

Identification of HIV Rapid Mutations Using Differences in Nucleotide Distribution over Time

Mutation is the driving force of species evolution, which may change the genetic information of organisms and obtain selective competitive advantages to adapt to environmental changes. It may change the structure or function of translated proteins, and cause abnormal cell operation, a variety of diseases and even cancer. Therefore, it is particularly important to identify gene regions with high mutations. Mutations will cause changes in nucleotide distribution, which can be characterized by natural vectors globally. Based on natural vectors, we propose a mathematical formula for measuring the difference in nucleotide distribution over time to investigate the mutations of human immunodeficiency virus. The studied dataset is from public databases and includes gene sequences from twenty HIV-infected patients. The results show that the mutation rate of the nine major genes or gene segment regions in the genome exhibits discrepancy during the infected period, and the Env gene has the fastest mutation rate. We deduce that the peak of virus mutation has a close temporal relationship with viral divergence and diversity. The mutation study of HIV is of great significance to clinical diagnosis and drug design.

MathFeature: feature extraction package for DNA, RNA and protein sequences based on mathematical descriptors

One of the main challenges in applying machine learning algorithms to biological sequence data is how to numerically represent a sequence in a numeric input vector. Feature extraction techniques capable of extracting numerical information from biological sequences have been reported in the literature. However, many of these techniques are not available in existing packages, such as mathematical descriptors. This paper presents a new package, MathFeature, which implements mathematical descriptors able to extract relevant numerical information from biological sequences, i.e. DNA, RNA and proteins (prediction of structural features along the primary sequence of amino acids). MathFeature makes available 20 numerical feature extraction descriptors based on approaches found in the literature, e.g. multiple numeric mappings, genomic signal processing, chaos game theory, entropy and complex networks. MathFeature also allows the extraction of alternative features, complementing the existing packages. To ensure that our descriptors are robust and to assess their relevance, experimental results are presented in nine case studies. According to these results, the features extracted by MathFeature showed high performance (0.6350-0.9897, accuracy), both applying only mathematical descriptors, but also hybridization with well-known descriptors in the literature. Finally, through MathFeature, we overcame several studies in eight benchmark datasets, exemplifying the robustness and viability of the proposed package. MathFeature has advanced in the area by bringing descriptors not available in other packages, as well as allowing non-experts to use feature extraction techniques.

The Resolved Mutual Information Function as a Structural Fingerprint of Biomolecular Sequences for Interpretable Machine Learning Classifiers

In the present article we propose the application of variants of the mutual information function as characteristic fingerprints of biomolecular sequences for classification analysis. In particular, we consider the resolved mutual information functions based on Shannon-, Rényi-, and Tsallis-entropy. In combination with interpretable machine learning classifier models based on generalized learning vector quantization, a powerful methodology for sequence classification is achieved which allows substantial knowledge extraction in addition to the high classification ability due to the model-inherent robustness. Any potential (slightly) inferior performance of the used classifier is compensated by the additional knowledge provided by interpretable models. This knowledge may assist the user in the analysis and understanding of the used data and considered task. After theoretical justification of the concepts, we demonstrate the approach for various example data sets covering different areas in biomolecular sequence analysis.

Advances in the computational analysis of SARS-COV2 genome

Given a data-set of Ribonucleic acid (RNA) sequences we can infer the phylogenetics of the samples and tackle the information for scientific purposes. Based on current data and knowledge, the SARS-CoV-2 seemingly mutates much more slowly than the influenza virus that causes seasonal flu. However, very recent evolution poses some doubts about such conjecture and shadows the out-coming light of people vaccination. This paper adopts mathematical and computational tools for handling the challenge of analyzing the data-set of different clades of the severe acute respiratory syndrome virus-2 (SARS-CoV-2). On one hand, based on the mathematical paraphernalia of tools, the concept of distance associated with the Kolmogorov complexity and Shannon information theories, as well as with the Hamming scheme, are considered. On the other, advanced data processing computational techniques, such as, data compression, clustering and visualization, are borrowed for tackling the problem. The results of the synergistic approach reveal the complex time dynamics of the evolutionary process and may help to clarify future directions of the SARS-CoV-2 evolution.

Geometric construction of viral genome space and its applications

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The first construction of viral genome space.

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The first demonstration of the convex hull principle of genomes.

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The first definition of a natural metric to describe the geometry of genome space.

Understanding the relationships between genomic sequences is essential to the classification and characterization of living beings. The classes and characteristics of an organism can be identified in the corresponding genome space. In the genome space, the natural metric is important to describe the distribution of genomes. Therefore, the similarity of two biological sequences can be measured. Here, we report that all of the viral genomes are in 32-dimensional Euclidean space, in which the natural metric is the weighted summation of Euclidean distance of k-mer natural vectors. The classification of viral genomes in the constructed genome space further proves the convex hull principle of taxonomy, which states that convex hulls of different families are mutually disjoint. This study provides a novel geometric perspective to describe the genome sequences.

Uncovering Signals from the Coronavirus Genome

A signal analysis of the complete genome sequenced for coronavirus variants of concern—B.1.1.7 (Alpha), B.1.135 (Beta) and P1 (Gamma)—and coronavirus variants of interest—B.1.429–B.1.427 (Epsilon) and B.1.525 (Eta)—is presented using open GISAID data. We deal with a certain new type of finite alternating sum series having independently distributed terms associated with binary (0,1) indicators for the nucleotide bases. Our method provides additional information to conventional similarity comparisons via alignment methods and Fourier Power Spectrum approaches. It leads to uncover distinctive patterns regarding the intrinsic data organization of complete genomics sequences according to its progression along the nucleotide bases position. The present new method could be useful for the bioinformatics surveillance and dynamics of coronavirus genome variants.

Learning vector quantization as an interpretable classifier for the detection of SARS-CoV-2 types based on their RNA sequences

We present an approach to discriminate SARS-CoV-2 virus types based on their RNA sequence descriptions avoiding a sequence alignment. For that purpose, sequences are preprocessed by feature extraction and the resulting feature vectors are analyzed by prototype-based classification to remain interpretable. In particular, we propose to use variants of learning vector quantization (LVQ) based on dissimilarity measures for RNA sequence data. The respective matrix LVQ provides additional knowledge about the classification decisions like discriminant feature correlations and, additionally, can be equipped with easy to realize reject options for uncertain data. Those options provide self-controlled evidence, i.e., the model refuses to make a classification decision if the model evidence for the presented data is not sufficient. This model is first trained using a GISAID dataset with given virus types detected according to the molecular differences in coronavirus populations by phylogenetic tree clustering. In a second step, we apply the trained model to another but unlabeled SARS-CoV-2 virus dataset. For these data, we can either assign a virus type to the sequences or reject atypical samples. Those rejected sequences allow to speculate about new virus types with respect to nucleotide base mutations in the viral sequences. Moreover, this rejection analysis improves model robustness. Last but not least, the presented approach has lower computational complexity compared to methods based on (multiple) sequence alignment.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00521-021-06018-2.

Feature extraction approaches for biological sequences: a comparative study of mathematical features

As consequence of the various genomic sequencing projects, an increasing volume of biological sequence data is being produced. Although machine learning algorithms have been successfully applied to a large number of genomic sequence-related problems, the results are largely affected by the type and number of features extracted. This effect has motivated new algorithms and pipeline proposals, mainly involving feature extraction problems, in which extracting significant discriminatory information from a biological set is challenging. Considering this, our work proposes a new study of feature extraction approaches based on mathematical features (numerical mapping with Fourier, entropy and complex networks). As a case study, we analyze long non-coding RNA sequences. Moreover, we separated this work into three studies. First, we assessed our proposal with the most addressed problem in our review, e.g. lncRNA and mRNA; second, we also validate the mathematical features in different classification problems, to predict the class of lncRNA, e.g. circular RNAs sequences; third, we analyze its robustness in scenarios with imbalanced data. The experimental results demonstrated three main contributions: first, an in-depth study of several mathematical features; second, a new feature extraction pipeline; and third, its high performance and robustness for distinct RNA sequence classification. Availability:  https://github.com/Bonidia/FeatureExtraction_BiologicalSequences.

Analysis of the Hosts and Transmission Paths of SARS-CoV-2 in the COVID-19 Outbreak

The severe respiratory disease COVID-19 was initially reported in Wuhan, China, in December 2019, and spread into many provinces from Wuhan. The corresponding pathogen was soon identified as a novel coronavirus named SARS-CoV-2 (formerly, 2019-nCoV). As of 2 May, 2020, over 3 million COVID-19 cases had been confirmed, and 235,290 deaths had been reported globally, and the numbers are still increasing. It is important to understand the phylogenetic relationship between SARS-CoV-2 and known coronaviruses, and to identify its hosts for preventing the next round of emergency outbreak. In this study, we employ an effective alignment-free approach, the Natural Vector method, to analyze the phylogeny and classify the coronaviruses based on genomic and protein data. Our results show that SARS-CoV-2 is closely related to, but distinct from the SARS-CoV branch. By analyzing the genetic distances from the SARS-CoV-2 strain to the coronaviruses residing in animal hosts, we establish that the most possible transmission path originates from bats to pangolins to humans.

Computational analysis of the SARS-CoV-2 and other viruses based on the Kolmogorov's complexity and Shannon's information theories

This paper tackles the information of 133 RNA viruses available in public databases under the light of several mathematical and computational tools. First, the formal concepts of distance metrics, Kolmogorov complexity and Shannon information are recalled. Second, the computational tools available presently for tackling and visualizing patterns embedded in datasets, such as the hierarchical clustering and the multidimensional scaling, are discussed. The synergies of the common application of the mathematical and computational resources are then used for exploring the RNA data, cross-evaluating the normalized compression distance, entropy and Jensen-Shannon divergence, versus representations in two and three dimensions. The results of these different perspectives give extra light in what concerns the relations between the distinct RNA viruses.

Measuring Similarity among Protein Sequences Using a New Descriptor

The comparison of protein sequences according to similarity is a fundamental aspect of today's biomedical research. With the developments of sequencing technologies, a large number of protein sequences increase exponentially in the public databases. Famous sequences' comparison methods are alignment based. They generally give excellent results when the sequences under study are closely related and they are time consuming. Herein, a new alignment-free method is introduced. Our technique depends on a new graphical representation and descriptor. The graphical representation of protein sequence is a simple way to visualize protein sequences. The descriptor compresses the primary sequence into a single vector composed of only two values. Our approach gives good results with both short and long sequences within a little computation time. It is applied on nine beta globin, nine ND5 (NADH dehydrogenase subunit 5), and 24 spike protein sequences. Correlation and significance analyses are also introduced to compare our similarity/dissimilarity results with others' approaches, results, and sequence homology.

SWSPM: A Novel Alignment-Free DNA Comparison Method Based on Signal Processing Approaches

Computing similarity between 2 nucleotide sequences is one of the fundamental problems in bioinformatics. Current methods are based mainly on 2 major approaches: (1) sequence alignment, which is computationally expensive, and (2) faster, but less accurate, alignment-free methods based on various statistical summaries, for example, short word counts. We propose a new distance measure based on mathematical transforms from the domain of signal processing. To tolerate large-scale rearrangements in the sequences, the transform is computed across sliding windows. We compare our method on several data sets with current state-of-art alignment-free methods. Our method compares favorably in terms of accuracy and outperforms other methods in running time and memory requirements. In addition, it is massively scalable up to dozens of processing units without the loss of performance due to communication overhead. Source files and sample data are available at https://bitbucket.org/fiitstubioinfo/swspm/src.

A Novel Approach to Clustering Genome Sequences Using Inter-nucleotide Covariance

Classification of DNA sequences is an important issue in the bioinformatics study, yet most existing methods for phylogenetic analysis including Multiple Sequence Alignment (MSA) are time-consuming and computationally expensive. The alignment-free methods are popular nowadays, whereas the manual intervention in those methods usually decreases the accuracy. Also, the interactions among nucleotides are neglected in most methods. Here we propose a new Accumulated Natural Vector (ANV) method which represents each DNA sequence by a point in ℝ¹⁸. By calculating the Accumulated Indicator Functions of nucleotides, we can further find an Accumulated Natural Vector for each sequence. This new Accumulated Natural Vector not only can capture the distribution of each nucleotide, but also provide the covariance among nucleotides. Thus global comparison of DNA sequences or genomes can be done easily in ℝ¹⁸. The tests of ANV of datasets of different sizes and types have proved the accuracy and time-efficiency of the new proposed ANV method.

ML-DSP: Machine Learning with Digital Signal Processing for ultrafast, accurate, and scalable genome classification at all taxonomic levels

Background

Although software tools abound for the comparison, analysis, identification, and classification of genomic sequences, taxonomic classification remains challenging due to the magnitude of the datasets and the intrinsic problems associated with classification. The need exists for an approach and software tool that addresses the limitations of existing alignment-based methods, as well as the challenges of recently proposed alignment-free methods.

Results

We propose a novel combination of supervised Machine Learning with Digital Signal Processing, resulting in ML-DSP: an alignment-free software tool for ultrafast, accurate, and scalable genome classification at all taxonomic levels. We test ML-DSP by classifying 7396 full mitochondrial genomes at various taxonomic levels, from kingdom to genus, with an average classification accuracy of >97%.

A quantitative comparison with state-of-the-art classification software tools is performed, on two small benchmark datasets and one large 4322 vertebrate mtDNA genomes dataset. Our results show that ML-DSP overwhelmingly outperforms the alignment-based software MEGA7 (alignment with MUSCLE or CLUSTALW) in terms of processing time, while having comparable classification accuracies for small datasets and superior accuracies for the large dataset. Compared with the alignment-free software FFP (Feature Frequency Profile), ML-DSP has significantly better classification accuracy, and is overall faster.

We also provide preliminary experiments indicating the potential of ML-DSP to be used for other datasets, by classifying 4271 complete dengue virus genomes into subtypes with 100% accuracy, and 4,710 bacterial genomes into phyla with 95.5% accuracy.

Lastly, our analysis shows that the “Purine/Pyrimidine”, “Just-A” and “Real” numerical representations of DNA sequences outperform ten other such numerical representations used in the Digital Signal Processing literature for DNA classification purposes.

Conclusions

Due to its superior classification accuracy, speed, and scalability to large datasets, ML-DSP is highly relevant in the classification of newly discovered organisms, in distinguishing genomic signatures and identifying their mechanistic determinants, and in evaluating genome integrity.

Alignment-Free Analyses of Nucleic Acid Sequences Using Graphical Representation (with Special Reference to Pandemic Bird Flu and Swine Flu)

The exponential growth in database of bio-molecular sequences have spawned many approaches towards storage, retrieval, classification and analyses requirements. Alignment-free techniques such as graphical representations and numerical characterisation (GRANCH) methods have enabled some detailed analyses of large sequences and found a number of different applications in the eukaryotic and prokaryotic domain. In particular, recalling the history of pandemic influenza in brief, we have followed the progress of viral infections such as bird flu of 1997 onwards and determined that the virus can spread conserved over space and time, that influenza virus can undergo fairly conspicuous recombination-like events in segmented genes, that certain segments of the neuraminidase and hemagglutinin surface proteins remain conserved and can be targeted for peptide vaccines. We recount in some detail a few of the representative GRANCH techniques to provide a glimpse of how these methods are used in formulating quantitative sequence descriptors to analyse DNA, RNA and protein sequences to derive meaningful results. Finally, we survey the surveillance techniques with a special reference to how the GRANCH techniques can be used for the purpose and recount the forecasts made of possible metamorphosis of pandemic bird flu to pandemic human infecting agents.

Detecting Periodicities in Eukaryotic Genomes by Ramanujan Fourier Transform

Ramanujan Fourier transform (RFT) nowadays is becoming a popular signal processing method. RFT is used to detect periodicities in exons and introns of eukaryotic genomes in this article. Genomic sequences of nine species were analyzed. The highest peak in the spectrum amplitude corresponding to each exon or intron is regarded as the significant signal. Accordingly, the periodicity corresponding to the significant signal can be also regarded as a valuable periodicity. Exons and introns have different periodic phenomena. The computational results reveal that the 2-, 3-, 4-, and 6-base periodicities of exons and introns are four kinds of important periodicities based on RFT. It is the first time that the 2-base periodicity of introns is discovered through signal processing method. The frequencies of the 2-base periodicity and the 3-base periodicity occurrence are polar opposite between the exons and the introns. With regard to the cyclicality of the Ramanujan sums, which is the base function of the transformation, RFT is suggested for studying the periodic features of dinucleotides, trinucleotides, and q nucleotides.

A new method to cluster genomes based on cumulative Fourier power spectrum

Analyzing phylogenetic relationships using mathematical methods has always been of importance in bioinformatics. Quantitative research may interpret the raw biological data in a precise way. Multiple Sequence Alignment (MSA) is used frequently to analyze biological evolutions, but is very time-consuming. When the scale of data is large, alignment methods cannot finish calculation in reasonable time. Therefore, we present a new method using moments of cumulative Fourier power spectrum in clustering the DNA sequences. Each sequence is translated into a vector in Euclidean space. Distances between the vectors can reflect the relationships between sequences. The mapping between the spectra and moment vector is one-to-one, which means that no information is lost in the power spectra during the calculation. We cluster and classify several datasets including Influenza A, primates, and human rhinovirus (HRV) datasets to build up the phylogenetic trees. Results show that the new proposed cumulative Fourier power spectrum is much faster and more accurately than MSA and another alignment-free method known as k-mer. The research provides us new insights in the study of phylogeny, evolution, and efficient DNA comparison algorithms for large genomes. The computer programs of the cumulative Fourier power spectrum are available at GitHub (https://github.com/YaulabTsinghua/cumulative-Fourier-power-spectrum).

A novel fast vector method for genetic sequence comparison

With sharp increasing in biological sequences, the traditional sequence alignment methods become unsuitable and infeasible. It motivates a surge of fast alignment-free techniques for sequence analysis. Among these methods, many sorts of feature vector methods are established and applied to reconstruction of species phylogeny. The vectors basically consist of some typical numerical features for certain biological problems. The features may come from the primary sequences, secondary or three dimensional structures of macromolecules. In this study, we propose a novel numerical vector based on only primary sequences of organism to build their phylogeny. Three chemical and physical properties of primary sequences: purine, pyrimidine and keto are also incorporated to the vector. Using each property, we convert the nucleotide sequence into a new sequence consisting of only two kinds of letters. Therefore, three sequences are constructed according to the three properties. For each letter of each sequence we calculate the number of the letter, the average position of the letter and the variation of the position of the letter appearing in the sequence. Tested on several datasets related to mammals, viruses and bacteria, this new tool is fast in speed and accurate for inferring the phylogeny of organisms.

A coevolution analysis for identifying protein-protein interactions by Fourier transform

Protein-protein interactions (PPIs) play key roles in life processes, such as signal transduction, transcription regulations, and immune response, etc. Identification of PPIs enables better understanding of the functional networks within a cell. Common experimental methods for identifying PPIs are time consuming and expensive. However, recent developments in computational approaches for inferring PPIs from protein sequences based on coevolution theory avoid these problems. In the coevolution theory model, interacted proteins may show coevolutionary mutations and have similar phylogenetic trees. The existing coevolution methods depend on multiple sequence alignments (MSA); however, the MSA-based coevolution methods often produce high false positive interactions. In this paper, we present a computational method using an alignment-free approach to accurately detect PPIs and reduce false positives. In the method, protein sequences are numerically represented by biochemical properties of amino acids, which reflect the structural and functional differences of proteins. Fourier transform is applied to the numerical representation of protein sequences to capture the dissimilarities of protein sequences in biophysical context. The method is assessed for predicting PPIs in Ebola virus. The results indicate strong coevolution between the protein pairs (NP-VP24, NP-VP30, NP-VP40, VP24-VP30, VP24-VP40, and VP30-VP40). The method is also validated for PPIs in influenza and E.coli genomes. Since our method can reduce false positive and increase the specificity of PPI prediction, it offers an effective tool to understand mechanisms of disease pathogens and find potential targets for drug design. The Python programs in this study are available to public at URL (https://github.com/cyinbox/PPI).

A Novel Method for Alignment-free DNA Sequence Similarity Analysis Based on the Characterization of Complex Networks

Determination of sequence similarity is one of the major steps in computational phylogenetic studies. One of the major tasks of computational biologists is to develop novel mathematical descriptors for similarity analysis. DNA clustering is an important technology that automatically identifies inherent relationships among large-scale DNA sequences. The comparison between the DNA sequences of different species helps determine phylogenetic relationships among species. Alignment-free approaches have continuously gained interest in various sequence analysis applications such as phylogenetic inference and metagenomic classification/clustering, particularly for large-scale sequence datasets. Here, we construct a novel and simple mathematical descriptor based on the characterization of cis sequence complex DNA networks. This new approach is based on a code of three cis nucleotides in a gene that could code for an amino acid. In particular, for each DNA sequence, we will set up a cis sequence complex network that will be used to develop a characterization vector for the analysis of mitochondrial DNA sequence phylogenetic relationships among nine species. The resulting phylogenetic relationships among the nine species were determined to be in agreement with the actual situation.

Periodic power spectrum with applications in detection of latent periodicities in DNA sequences

Periodic elements play important roles in genomic structures and functions, yet some complex periodic elements in genomes are difficult to detect by conventional methods such as digital signal processing and statistical analysis. We propose a periodic power spectrum (PPS) method for analyzing periodicities of DNA sequences. The PPS method employs periodic nucleotide distributions of DNA sequences and directly calculates power spectra at specific periodicities. The magnitude of a PPS reflects the strength of a signal on periodic positions. In comparison with Fourier transform, the PPS method avoids spectral leakage, and reduces background noise that appears high in Fourier power spectrum. Thus, the PPS method can effectively capture hidden periodicities in DNA sequences. Using a sliding window approach, the PPS method can precisely locate periodic regions in DNA sequences. We apply the PPS method for detection of hidden periodicities in different genome elements, including exons, microsatellite DNA sequences, and whole genomes. The results show that the PPS method can minimize the impact of spectral leakage and thus capture true hidden periodicities in genomes. In addition, performance tests indicate that the PPS method is more effective and efficient than a fast Fourier transform. The computational complexity of the PPS algorithm is [Formula: see text]. Therefore, the PPS method may have a broad range of applications in genomic analysis. The MATLAB programs for implementing the PPS method are available from MATLAB Central ( http://www.mathworks.com/matlabcentral/fileexchange/55298 ).

Progressive alignment of genomic signals by multiple dynamic time warping

This paper presents the utilization of progressive alignment principle for positional adjustment of a set of genomic signals with different lengths. The new method of multiple alignment of signals based on dynamic time warping is tested for the purpose of evaluating the similarity of different length genes in phylogenetic studies. Two sets of phylogenetic markers were used to demonstrate the effectiveness of the evaluation of intraspecies and interspecies genetic variability. The part of the proposed method is modification of pairwise alignment of two signals by dynamic time warping with using correlation in a sliding window. The correlation based dynamic time warping allows more accurate alignment dependent on local homologies in sequences without the need of scoring matrix or evolutionary models, because mutual similarities of residues are included in the numerical code of signals.

An improved model for whole genome phylogenetic analysis by Fourier transform

DNA sequence similarity comparison is one of the major steps in computational phylogenetic studies. The sequence comparison of closely related DNA sequences and genomes is usually performed by multiple sequence alignments (MSA). While the MSA method is accurate for some types of sequences, it may produce incorrect results when DNA sequences undergone rearrangements as in many bacterial and viral genomes. It is also limited by its computational complexity for comparing large volumes of data. Previously, we proposed an alignment-free method that exploits the full information contents of DNA sequences by Discrete Fourier Transform (DFT), but still with some limitations. Here, we present a significantly improved method for the similarity comparison of DNA sequences by DFT. In this method, we map DNA sequences into 2-dimensional (2D) numerical sequences and then apply DFT to transform the 2D numerical sequences into frequency domain. In the 2D mapping, the nucleotide composition of a DNA sequence is a determinant factor and the 2D mapping reduces the nucleotide composition bias in distance measure, and thus improving the similarity measure of DNA sequences. To compare the DFT power spectra of DNA sequences with different lengths, we propose an improved even scaling algorithm to extend shorter DFT power spectra to the longest length of the underlying sequences. After the DFT power spectra are evenly scaled, the spectra are in the same dimensionality of the Fourier frequency space, then the Euclidean distances of full Fourier power spectra of the DNA sequences are used as the dissimilarity metrics. The improved DFT method, with increased computational performance by 2D numerical representation, can be applicable to any DNA sequences of different length ranges. We assess the accuracy of the improved DFT similarity measure in hierarchical clustering of different DNA sequences including simulated and real datasets. The method yields accurate and reliable phylogenetic trees and demonstrates that the improved DFT dissimilarity measure is an efficient and effective similarity measure of DNA sequences. Due to its high efficiency and accuracy, the proposed DFT similarity measure is successfully applied on phylogenetic analysis for individual genes and large whole bacterial genomes.

Set of rules for genomic signal downsampling

Comparison and classification of organisms based on molecular data is an important task of computational biology, since at least parts of DNA sequences for many organisms are available. Unfortunately, methods for comparison are computationally very demanding, suitable only for short sequences. In this paper, we focus on the redundancy of genetic information stored in DNA sequences. We proposed rules for downsampling of DNA signals of cumulated phase. According to the length of an original sequence, we are able to significantly reduce the amount of data with only slight loss of original information. Dyadic wavelet transform was chosen for fast downsampling with minimum influence on signal shape carrying the biological information. We proved the usability of such new short signals by measuring percentage deviation of pairs of original and downsampled signals while maintaining spectral power of signals. Minimal loss of biological information was proved by measuring the Robinson-Foulds distance between pairs of phylogenetic trees reconstructed from the original and downsampled signals. The preservation of inter-species and intra-species information makes these signals suitable for fast sequence identification as well as for more detailed phylogeny reconstruction.

Representation of DNA sequences in genetic codon context with applications in exon and intron prediction

To apply digital signal processing (DSP) methods to analyze DNA sequences, the sequences first must be specially mapped into numerical sequences. Thus, effective numerical mappings of DNA sequences play key roles in the effectiveness of DSP-based methods such as exon prediction. Despite numerous mappings of symbolic DNA sequences to numerical series, the existing mapping methods do not include the genetic coding features of DNA sequences. We present a novel numerical representation of DNA sequences using genetic codon context (GCC) in which the numerical values are optimized by simulation annealing to maximize the 3-periodicity signal to noise ratio (SNR). The optimized GCC representation is then applied in exon and intron prediction by Short-Time Fourier Transform (STFT) approach. The results show the GCC method enhances the SNR values of exon sequences and thus increases the accuracy of predicting protein coding regions in genomes compared with the commonly used 4D binary representation. In addition, this study offers a novel way to reveal specific features of DNA sequences by optimizing numerical mappings of symbolic DNA sequences.