Chaos Game Representation Research Articles

Genomic image representation of human coronavirus sequences for COVID-19 detection

Coronavirus (CoV) disease 2019 (COVID-19) is a severe pandemic affecting millions worldwide. Due to its rapid evolution, researchers have been working on developing diagnostic approaches to suppress its spread. This study presents an effective automated approach based on genomic image processing (GIP) techniques to rapidly detect COVID-19, among other human CoV diseases, with high acceptable accuracy. The GIP technique was applied as follows: first, genomic graphical mapping techniques were used to convert the genome sequences into genomic grayscale images. The frequency chaos game representation (FCGR) and single gray-level representation (SGLR) techniques were used in this investigation. Then, several statistical features were obtained from the images to train and test many classifiers, including the k-nearest neighbors (KNN). This study aimed to determine the efficacy of the FCGR (with different orders) and SGLR images for accurately detecting COVID-19,using a dataset containing both partial and complete genome sequences. The results recommended the fourth-order FCGR image as a proper genomic image for extracting statistical features and achieving accurate classification. Furthermore, the results showed that KNN achieved an overall accuracy of 99.39% in detecting COVID-19, among other human CoV diseases, with 99.48% precision, 99.31% sensitivity, 99.47% specificity, 0.99 F1-score, and 0.99 Matthew's correlation coefficient.

PSuc-FFSEA: Predicting Lysine Succinylation Sites in Proteins Based on Feature Fusion and Stacking Ensemble Algorithm.

Being a new type of widespread protein post-translational modifications discovered in recent years, succinylation plays a key role in protein conformational regulation and cellular function regulation. Numerous studies have shown that succinylation modifications are closely associated with the development of many diseases. In order to gain insight into the mechanism of succinylation, it is vital to identify lysine succinylation sites. However, experimental identification of succinylation sites is time-consuming and laborious, and traditional identification tools are unable to meet the rapid growth of datasets. Therefore, to solve this problem, we developed a new predictor named pSuc-FFSEA, which can predict succinylation sites in protein sequences by feature fusion and stacking ensemble algorithm. Specifically, the sequence information and physicochemical properties were first extracted using EBGW, One-Hot, continuous bag-of-words, chaos game representation, and AAF_DWT. Following that, feature selection was performed, which applied LASSO to select the optimal subset of features for the classifier, and then, stacking ensemble classifier was designed using two-layer stacking ensemble, selecting three classifiers, SVM, broad learning system and LightGBM classifier, as the base classifiers of the first layer, using logistic regression classifier as the meta classifier of the second layer. In order to further improve the model prediction accuracy and reduce the computational effort, bayesian optimization algorithm and grid search algorithm were utilized to optimize the hyperparameters of the classifier. Finally, the results of rigorous 10-fold cross-validation indicated our predictor showed excellent robustness and performed better than the previous prediction tools, which achieved an average prediction accuracy of 0.7773 ± 0.0120. Besides, for the convenience of the most experimental scientists, a user-friendly and comprehensive web-server for pSuc-FFSEA has been established at https://bio.cangmang.xyz/pSuc-FFSEA, by which one can easily obtain the expected data and results without going through the complicated mathematics.

Mitochondrial DNA Profiling by Fractal Lacunarity to Characterize the Senescent Phenotype as Normal Aging or Pathological Aging

Biocomplexity, chaos, and fractality can explain the heterogeneity of aging individuals by regarding longevity as a “secondary product” of the evolution of a dynamic nonlinear system. Genetic-environmental interactions drive the individual senescent phenotype toward normal, pathological, or successful aging. Mitochondrial dysfunctions and mitochondrial DNA (mtDNA) mutations represent a possible mechanism shared by disease(s) and the aging process. This study aims to characterize the senescent phenotype and discriminate between normal (nA) and pathological (pA) aging by mtDNA mutation profiling. MtDNA sequences from hospitalized and non-hospitalized subjects (age-range: 65–89 years) were analyzed and compared to the revised Cambridge Reference Sequence (rCRS). Fractal properties of mtDNA sequences were displayed by chaos game representation (CGR) method, previously modified to deal with heteroplasmy. Fractal lacunarity analysis was applied to characterize the senescent phenotype on the basis of mtDNA sequence mutations. Lacunarity parameter β, from our hyperbola model function, was statistically different (p < 0.01) between the nA and pA groups. Parameter β cut-off value at 1.26 × 10−3 identifies 78% nA and 80% pA subjects. This also agrees with the presence of MT-CO gene variants, peculiar to nA (C9546m, 83%) and pA (T9900w, 80%) mtDNA, respectively. Fractal lacunarity can discriminate the senescent phenotype evolving as normal or pathological aging by individual mtDNA mutation profile.

A new method in encryption of gray scale images using chaos game representation

A new method in encryption of gray scale images using chaos game representation

Numerical Characterization of DNA Sequences for Alignment-free Sequence Comparison - A Review.

Biological macromolecules, namely, DNA, RNA, and protein, have their building blocks organized in a particular sequence and the sequential arrangement encodes the evolutionary history of the organism (species). Hence, biological sequences have been used for studying evolutionary relationships among the species. This is usually carried out by Multiple Sequence Algorithms (MSA). Due to certain limitations of MSA, alignment-free sequence comparison methods were developed. The present review is on alignment-free sequence comparison methods carried out using the numerical characterization of DNA sequences. The graphical representation of DNA sequences by chaos game representation and other 2-dimensional and 3-dimensional methods are discussed. The evolution of numerical characterization from the various graphical representations and the application of the DNA invariants thus computed in phylogenetic analysis are presented. The extension of computing molecular descriptors in chemometrics to the calculation of a new set of DNA invariants and their use in alignment-free sequence comparison in an N-dimensional space and construction of phylogenetic trees are also reviewed. The phylogenetic tress constructed by the alignment-free sequence comparison methods using DNA invariants were found to be better than those constructed using alignment-based tools such as PHLYIP and ClustalW. One of the graphical representation methods is now extended to study viral sequences of infectious diseases for the identification of conserved regions to design peptidebased vaccines by combining numerical characterization and graphical representation.

Fractal Analysis of DNA Sequences Using Frequency Chaos Game Representation and Small-Angle Scattering.

The fractal characteristics of DNA sequences are studied using the frequency chaos game representation (FCGR) and small-angle scattering (SAS) technique. The FCGR allows representation of the frequencies of occurrence of k-mers (oligonucleotides of length k) in the form of images. The numerically encoded data are then used in a SAS analysis to enhance hidden features in DNA sequences. It is shown that the simulated SAS intensity allows us to obtain the fractal dimensions and scaling factors at various scales. These structural parameters can be used to distinguish unambiguously between the scaling properties of complex hierarchical DNA sequences. The validity of this approach is illustrated on several sequences from: Escherichia coli, Mouse mitochondrion, Homo sapiens mitochondrion and Human cosmid.

Detection of intra-family coronavirus genome sequences through graphical representation and artificial neural network

In this study, chaos game representation (CGR) is introduced for investigating the pattern of genome sequences. It is an image representation of the genome for the overall visualization of the sequence. The CGR representation is a mapping technique that assigns each sequence base into the respective position in the two-dimension plane to portray the DNA sequence. Importantly, CGR provides one to one mapping to nucleotides as well as sequence. A coordinate of the CGR plane can tell the corresponding base and its location in the original genome. Therefore, the whole nucleotide sequence (until the current nucleotide) can be restored from the one point of the CGR. In this study, CGR coupled with artificial neural network (ANN) is introduced as a new way to represent the genome and to classify intra-coronavirus sequences. A hierarchy clustering study is done to validate the approach and found to be more than 90% accurate while comparing the result with the phylogenetic tree of the corresponding genomes. Interestingly, the method makes the genome sequence significantly shorter (more than 99% compressed) saving the data space while preserving the genome features.

DeLUCS: Deep learning for unsupervised clustering of DNA sequences.

We present a novel Deep Learning method for the Unsupervised Clustering of DNA Sequences (DeLUCS) that does not require sequence alignment, sequence homology, or (taxonomic) identifiers. DeLUCS uses Frequency Chaos Game Representations (FCGR) of primary DNA sequences, and generates “mimic” sequence FCGRs to self-learn data patterns (genomic signatures) through the optimization of multiple neural networks. A majority voting scheme is then used to determine the final cluster assignment for each sequence. The clusters learned by DeLUCS match true taxonomic groups for large and diverse datasets, with accuracies ranging from 77% to 100%: 2,500 complete vertebrate mitochondrial genomes, at taxonomic levels from sub-phylum to genera; 3,200 randomly selected 400 kbp-long bacterial genome segments, into clusters corresponding to bacterial families; three viral genome and gene datasets, averaging 1,300 sequences each, into clusters corresponding to virus subtypes. DeLUCS significantly outperforms two classic clustering methods (K-means++ and Gaussian Mixture Models) for unlabelled data, by as much as 47%. DeLUCS is highly effective, it is able to cluster datasets of unlabelled primary DNA sequences totalling over 1 billion bp of data, and it bypasses common limitations to classification resulting from the lack of sequence homology, variation in sequence length, and the absence or instability of sequence annotations and taxonomic identifiers. Thus, DeLUCS offers fast and accurate DNA sequence clustering for previously intractable datasets.

Evolutionary Relationship of Protein Sequences of SARS-CoV-2 and Other Viruses through Chaos Game Representation

Comparison between different biological sequences is a key step in bioinformatics when analyzing similarities of sequences and phylogenetic relationships. A method of graphically representing biological sequences known as Chaos Game Representation (CGR) has achieved many applications in the studies of bioinformatics. The key issue in the application of CGR is to extract as many useful features as possible from CGR. Initially, CGR was applied to DNA sequences, but in this paper, a CGR-based approach is used to extract suitable features for comparing protein sequences of SARS-CoV-2 and other viruses. For this aim, several viral protein sequences from 12 groups are considered and CGR centroid, amino acid frequency, compounded frequency, Shannon entropy, and Kullback-Lieber Discrimination Information are applied to find the inter-relationship among the sequences. The experimental results demonstrate the potential strengths of CGR-based method for examining the evolutionary relationship of protein sequences. Our method is powerful for extracting effective features from protein sequences, and therefore important in classifying proteins and inferring the phylogeny of viruses.

Bidirectional Long Short-Term Memory Network for Taxonomic Classification

Identifying and classifying Deoxyribonucleic Acid (DNA) sequences and their functions have been considered as the main challenges in bioinformatics. Advances in machine learning and Deep Learning (DL) techniques are expected to improve DNA sequence classification. Since the DNA sequence classification depends on analyzing textual data, Bidirectional Long Short-Term Memory (BLSTM) algorithms are suitable for tackling this task. Generally, classifiers depend on the patterns to be processed and the pre-processing method. This paper is concerned with a new proposed classification framework based on Frequency Chaos Game Representation (FCGR) followed by Discrete Wavelet Transform (DWT) and BLSTM. Firstly, DNA strings are transformed into numerical matrices by FCGR. Then, the DWT is used instead of the pooling layer as a tool of data compression. The benefit of using the DWT is two-fold. It preserves the useful information only that enables the following BLSTM training, effectively. Besides, DWT adds more important details to the encoded sequences due to finding effective features in the DNA fragments. Finally, the BLSTM model is trained to classify the DNA sequences. Evaluation metrics such as F1 score and accuracy show that the proposed framework outperforms the state-of-the-art algorithms. Hence, it can be used in DNA classification applications.

Fractal construction of constrained code words for DNA storage systems

The use of complex biological molecules to solve computational problems is an emerging field at the interface between biology and computer science. There are two main categories in which biological molecules, especially DNA, are investigated as alternatives to silicon-based computer technologies. One is to use DNA as a storage medium, and the other is to use DNA for computing. Both strategies come with certain constraints. In the current study, we present a novel approach derived from chaos game representation for DNA to generate DNA code words that fulfill user-defined constraints, namely GC content, homopolymers, and undesired motifs, and thus, can be used to build codes for reliable DNA storage systems.

Prediction of antimicrobial resistance based on whole-genome sequencing and machine learning.

MotivationAntimicrobial resistance (AMR) is one of the biggest global problems threatening human and animal health. Rapid and accurate AMR diagnostic methods are thus very urgently needed. However, traditional antimicrobial susceptibility testing (AST) is time-consuming, low throughput and viable only for cultivable bacteria. Machine learning methods may pave the way for automated AMR prediction based on genomic data of the bacteria. However, comparing different machine learning methods for the prediction of AMR based on different encodings and whole-genome sequencing data without previously known knowledge remains to be done.ResultsIn this study, we evaluated logistic regression (LR), support vector machine (SVM), random forest (RF) and convolutional neural network (CNN) for the prediction of AMR for the antibiotics ciprofloxacin, cefotaxime, ceftazidime and gentamicin. We could demonstrate that these models can effectively predict AMR with label encoding, one-hot encoding and frequency matrix chaos game representation (FCGR encoding) on whole-genome sequencing data. We trained these models on a large AMR dataset and evaluated them on an independent public dataset. Generally, RFs and CNNs perform better than LR and SVM with AUCs up to 0.96. Furthermore, we were able to identify mutations that are associated with AMR for each antibiotic.Availability and implementationSource code in data preparation and model training are provided at GitHub website (https://github.com/YunxiaoRen/ML-iAMR).Supplementary informationSupplementary data are available at Bioinformatics online.

A Study of the International Stock Market Behavior During COVID-19 Pandemic Using a Driven Iterated Function System.

We propose a novel approach to visualize and compare financial markets across the globe using chaos game representation (CGR) of iterated function systems (IFS). We modified a fractal method, widely used in life sciences, and applied it to study the effect of COVID-19 on global financial markets. This modified driven IFS approach is used to generate compact fractal portraits of the financial markets in form of percentage CGR (PC) plots and subtraction percentage (SP) plots. The markets over different periods are compared and the difference is quantified through a parameter called the proximity (Pr) index. The reaction of the financial market across the globe and volatility to the current pandemic of COVID-19 is studied and modeled successfully. The imminent bearish and a surprise bullish pattern of the financial markets across the world is revealed by this fractal method and provides a new tool to study financial markets.

Harnessing the information theory and chaos game representation for pattern searching among essential and non-essential genes in Bacteria

Proteins encoded by genes are engaged in most of the processes within a cell. Typing a minimal set of genes required for survival is still a challenging task. Essential genes seem to be more conservative and are usually responsible for basic functions, for instance, genetic information flow or energy production. Despite persistent advances in experimental methods, computer predictions may constitute an important part of this investigation. Firstly, they may embrace a huge amount of data and provide some characteristic patterns. Furthermore, they enable scientists to build models for predicting essential genes which are not yet verified experimentally. Some papers indicate interesting dependencies within essential genes sequences using different computer models. In this paper, an author took a three-step analysis for a deeper understanding of the fundamentals of essential and non-essential genes. Beginning from a simple nucleotide composition and finishing at long-range correlations, presents some characteristic patterns that are expected to be developed in future studies.

Multifractal and cross-correlation analysis on mitochondrial genome sequences using chaos game representation

We characterized the multifractality and power-law cross-correlation of mitochondrial genomes of various species through the recently developed method which combines the chaos game representation theory and 2D-multifractal detrended cross-correlation analysis. In the present paper, we analyzed 32 mitochondrial genomes of different species and the obtained results show that all the analyzed data exhibit multifractal nature and power-law cross-correlation behaviour. Further, we performed a cluster analysis from the calculated scaling exponents to identify the class affiliation and its outcome is represented as a dendrogram. We suggest that this integrative approach may help the researchers to understand the phylogeny of any kingdom with their varying genome lengths and also this approach may find applications in characterizing the protein sequences, mRNA sequences, next-generation sequencing, and drug development, etc.

Comparative analysis and prediction of nucleosome positioning using integrative feature representation and machine learning algorithms

BackgroundNucleosome plays an important role in the process of genome expression, DNA replication, DNA repair and transcription. Therefore, the research of nucleosome positioning has invariably received extensive attention. Considering the diversity of DNA sequence representation methods, we tried to integrate multiple features to analyze its effect in the process of nucleosome positioning analysis. This process can also deepen our understanding of the theoretical analysis of nucleosome positioning.ResultsHere, we not only used frequency chaos game representation (FCGR) to construct DNA sequence features, but also integrated it with other features and adopted the principal component analysis (PCA) algorithm. Simultaneously, support vector machine (SVM), extreme learning machine (ELM), extreme gradient boosting (XGBoost), multilayer perceptron (MLP) and convolutional neural networks (CNN) are used as predictors for nucleosome positioning prediction analysis, respectively. The integrated feature vector prediction quality is significantly superior to a single feature. After using principal component analysis (PCA) to reduce the feature dimension, the prediction quality of H. sapiens dataset has been significantly improved.ConclusionsComparative analysis and prediction on H. sapiens, C. elegans, D. melanogaster and S. cerevisiae datasets, demonstrate that the application of FCGR to nucleosome positioning is feasible, and we also found that integrative feature representation would be better.

Structural classification of proteins based on the computationally efficient recurrence quantification analysis and horizontal visibility graphs.

Protein structural class prediction is one of the most significant problems in bioinformatics, as it has a prominent role in understanding the function and evolution of proteins. Designing a computationally efficient but at the same time accurate prediction method remains a pressing issue, especially for sequences that we cannot obtain a sufficient amount of homologous information from existing protein sequence databases. Several studies demonstrate the potential of utilizing chaos game representation along with time series analysis tools such as recurrence quantification analysis, complex networks, horizontal visibility graphs (HVG) and others. However, the majority of existing works involve a large amount of features and they require an exhaustive, time consuming search of the optimal parameters. To address the aforementioned problems, this work adopts the generalized multidimensional recurrence quantification analysis (GmdRQA) as an efficient tool that enables to process concurrently a multidimensional time series and reduce the number of features. In addition, two data-driven algorithms, namely average mutual information and false nearest neighbors, are utilized to define in a fast yet precise manner the optimal GmdRQA parameters. The classification accuracy is improved by the combination of GmdRQA with the HVG. Experimental evaluation on a real benchmark dataset demonstrates that our methods achieve similar performance with the state-of-the-art but with a smaller computational cost. The code to reproduce all the results is available at https://github.com/aretiz/protein_structure_classification/tree/main. Supplementary data are available at Bioinformatics online.

Applying frequency chaos game representation with perceptual image hashing to gene sequence phylogenetic analyses

As a very important research direction in the field of bioinformatics, sequence alignment plays a vital role in the research and development of biology. Converting genome sequence to graph by using frequency chaos game representation (FCGR) is an excellent gene sequence mapping technology, which can store rich genetic information into FCGR graphics. To each FCGR image, we construct its perceptual image hashing (PIH) matrix using the bicubic interpolation zooming. The difference of the perceptual hash matrix of each two images is calculated, and the clustering distance of the corresponding two gene sequences is represented by the differentials of the perceptual hash matrix. In this paper, we aligned and analyzed several typical genome sequence datasets including mammalian mitochondrial genes, human immunodeficiency virus 1 (HIV-1) and hepatitis E virus (HEV) to build their evolutionary trees. Experimental results showed that our PIH combining FCGR method (FCGR-PIH) has similar classification accuracy to the classical Clustal W sequence alignment method. Furthermore, 25 complete mitochondrial DNA sequences of cichlid fishes and 27 Escherichia coli/Shigella full genome sequences were selected from the AFproject test platform for tests. The performance benchmark rankings demonstrate the effectiveness of the FCGR-PIH algorithm and its potential for large-scale genome sequence analysis.

Involving FCGR images in studying fractality and multifractality in human chromosome 22 and bacteria complete genome

The frequency chaos game representation (FCGR) is a simple yet powerful visualization method of DNA sequences. It provides the possibility of representing genomes by images, revealing in such a way different fractal structures. In this paper, we perform a fractal and multifractal analysis of Human chromosome 22 and some complete genomes based on the FGCR image. We used the fractal dimension (FD) and the multifractality degree (ΔDq) to characterize and distinguish genomes. First, we construct the FCGR image with different orders of human chromosome 22. Next, we calculate the fractal dimension, the general dimension spectrum and the multifractal spectrum of each FCGR image using the box-counting method. Then, we examine the FCGR image fractal and multifractal characteristics impact on highlighting the existence of repetitive DNA sequences in human chromosome 22. We also observe the relationship between fractality and multifractality. After that, we apply this study to bacteria completes genomes and C.elegans chromosome I. The obtained results show that the multifractal spectra of all organisms studied are multifractal-like and chromosome 22 strong multifractality proves its richness of repetitive sequences. Also, we observed that with the increasing the FCGR order value, the multifractality grows and the fractal dimension lessens. Finally, by assigning to each sequence a point in two-dimensional space (FD, ΔDq), we obtained three classes of genomes. We can easily distinguish the human chromosome 22 from other genomes and Bacteria are almost close in the spaces (FD, ΔDq).

Symbolic Sequence Classification in the Fractal Space

Sequence classification has a range of applications and attracted a lot of attentions. Different from feature vectors, symbolic sequences have no explicit features. Due to this limitation, even with sophisticated feature selection techniques, the dimension of potential feature space could be very high, making classification methods hard to capture the nature of sequences. In this paper, we propose a novel scheme that first constructs a new lower dimensional representation space for symbolic sequences. Next, we carry out learning in this newly generated space rather than on the sequences. The first step is implemented with a chaos game representation, which converts a long sequence into a graphical form by applying an iterated function system on the input. For this reason, this new target space is referred as “fractal space” in this paper. The second step consists of carrying out sequence comparison and quantitative analysis with an alignment-free measure based on the holistic features from the sequences. This scheme is highly flexible and could permit high-performance implementation. The experimental results demonstrate the effectiveness and efficiency of our proposed approach.