Chaos game representation and its applications in bioinformatics

NeuralBeds: Neural embeddings for efficient DNA data compression and optimized similarity search

The availability of high throughput sequencing tools coupled with the declining costs in the production of DNA sequences has led to the generation of enormous amounts of omics data curated in several databases such as NCBI and EMBL. Identification of similar DNA sequences from these databases is one of the fundamental tasks in bioinformatics. It is essential for discovering homologous sequences in organisms, phylogenetic studies of evolutionary relationships among several biological entities, or detection of pathogens. Improving DNA similarity search is of outmost importance because of the increased complexity of the evergrowing repositories of sequences. Therefore, instead of using the conventional approach of comparing raw sequences, e.g., in fasta format, a numerical representation of the sequences can be used to calculate their similarities and optimize the search process. In this study, we analyzed different approaches for numerical embeddings, including Chaos Game Representation, hashing, and neural networks, and compared them with classical approaches such as principal component analysis. It turned out that neural networks generate embeddings that are able to capture the similarity between DNA sequences as a distance measure and outperform the other approaches on DNA similarity search, significantly.

CapsEnhancer: An Effective Computational Framework for Identifying Enhancers Based on Chaos Game Representation and Capsule Network

Enhancers are a class of noncoding DNA, serving as crucial regulatory elements in governing gene expression by binding to transcription factors. The identification of enhancers holds paramount importance in the field of biology. However, traditional experimental methods for enhancer identification demand substantial human and material resources. Consequently, there is a growing interest in employing computational methods for enhancer prediction. In this study, we propose a two-stage framework based on deep learning, termed CapsEnhancer, for the identification of enhancers and their strengths. CapsEnhancer utilizes chaos game representation to encode DNA sequences into unique images and employs a capsule network to extract local and global features from sequence "images". Experimental results demonstrate that CapsEnhancer achieves state-of-the-art performance in both stages. In the first and second stages, the accuracy surpasses the previous best methods by 8 and 3.5%, reaching accuracies of 94.5 and 95%, respectively. Notably, this study represents the pioneering application of computer vision methods to enhancer identification tasks. Our work not only contributes novel insights to enhancer identification but also provides a fresh perspective for other biological sequence analysis tasks.

Prioritizing cervical cancer candidate genes using chaos game and fractal-based time series approach

Cervical cancer is one of the most severe threats to women worldwide and holds fourth rank in lethality. It is estimated that 604, 127 cervical cancer cases have been reported in 2020 globally. With advancements in high throughput technologies and bioinformatics, several cervical candidate genes have been proposed for better therapeutic strategies. In this paper, we intend to prioritize the candidate genes that are involved in cervical cancer progression through a fractal time series-based cross-correlations approach. we apply the chaos game representation theory combining a two-dimensional multifractal detrended cross-correlations approach among the known and candidate genes involved in cervical cancer progression to prioritize the candidate genes. We obtained 16 candidate genes that showed cross-correlation with known cancer genes. Functional enrichment analysis of the candidate genes shows that they involve GO terms: biological processes, cell-cell junction assembly, cell-cell junction organization, regulation of cell shape, cortical actin cytoskeleton organization, and actomyosin structure organization. KEGG pathway analysis revealed genes' role in Rap1 signaling pathway, ErbB signaling pathway, MAPK signaling pathway, PI3K-Akt signaling pathway, mTOR signaling pathway, Acute myeloid leukemia, chronic myeloid leukemia, Breast cancer, Thyroid cancer, Bladder cancer, and Gastric cancer. Further, we performed survival analysis and prioritized six genes CDH2, PAIP1, BRAF, EPB41L3, OSMR, and RUNX1 as potential candidate genes for cervical cancer that has a crucial role in tumor progression. We found that our study through this integrative approach an efficient tool and paved a new way to prioritize the candidate genes and these genes could be evaluated experimentally for potential validation. We suggest this may be useful in analyzing the nucleotide sequences and protein sequences for clustering, classification, class affiliation, etc.

CGO-ensemble: Chaos game optimization algorithm-based fusion of deep neural networks for accurate Mpox detection

The rising global incidence of human Mpox cases necessitates prompt and accurate identification for effective disease control. Previous studies have predominantly delved into traditional ensemble methods for detection, we introduce a novel approach by leveraging a metaheuristic-based ensemble framework. In this research, we present an innovative CGO-Ensemble framework designed to elevate the accuracy of detecting Mpox infection in patients. Initially, we employ five transfer learning base models that integrate feature integration layers and residual blocks. These components play a crucial role in capturing significant features from the skin images, thereby enhancing the models' efficacy. In the next step, we employ a weighted averaging scheme to consolidate predictions generated by distinct models. To achieve the optimal allocation of weights for each base model in the ensemble process, we leverage the Chaos Game Optimization (CGO) algorithm. This strategic weight assignment enhances classification outcomes considerably, surpassing the performance of randomly assigned weights. Implementing this approach yields notably enhanced prediction accuracy compared to using individual models. We evaluate the effectiveness of our proposed approach through comprehensive experiments conducted on two widely recognized benchmark datasets: the Mpox Skin Lesion Dataset (MSLD) and the Mpox Skin Image Dataset (MSID). To gain insights into the decision-making process of the base models, we have performed Gradient Class Activation Mapping (Grad-CAM) analysis. The experimental results showcase the outstanding performance of the CGO-ensemble, achieving an impressive accuracy of 100% on MSLD and 94.16% on MSID. Our approach significantly outperforms other state-of-the-art optimization algorithms, traditional ensemble methods, and existing techniques in the context of Mpox detection on these datasets. These findings underscore the effectiveness and superiority of the CGO-Ensemble in accurately identifying Mpox cases, highlighting its potential in disease detection and classification.

CGRWDL: alignment-free phylogeny reconstruction method for viruses based on chaos game representation weighted by dynamical language model

Traditional alignment-based methods meet serious challenges in genome sequence comparison and phylogeny reconstruction due to their high computational complexity. Here, we propose a new alignment-free method to analyze the phylogenetic relationships (classification) among species. In our method, the dynamical language (DL) model and the chaos game representation (CGR) method are used to characterize the frequency information and the context information of k-mers in a sequence, respectively. Then for each DNA sequence or protein sequence in a dataset, our method converts the sequence into a feature vector that represents the sequence information based on CGR weighted by the DL model to infer phylogenetic relationships. We name our method CGRWDL. Its performance was tested on both DNA and protein sequences of 8 datasets of viruses to construct the phylogenetic trees. We compared the Robinson-Foulds (RF) distance between the phylogenetic tree constructed by CGRWDL and the reference tree by other advanced methods for each dataset. The results show that the phylogenetic trees constructed by CGRWDL can accurately classify the viruses, and the RF scores between the trees and the reference trees are smaller than that with other methods.

Changes in oscillatory patterns of microstate sequence in patients with first-episode psychosis

We aimed to utilize chaos game representation (CGR) for the investigation of microstate sequences and explore its potential as neurobiomarkers for psychiatric disorders. We applied our proposed method to a public dataset including 82 patients with first-episode psychosis (FEP) and 61 control subjects. Two time series were constructed: one using the microstate spacing distance in CGR and the other using complex numbers representing the microstate coordinates in CGR. Power spectral features of both time series and frequency matrix CGR (FCGR) were compared between groups and employed in a machine learning application. The four canonical microstates (A, B, C, and D) were identified using both shared and separate templates. Our results showed the microstate oscillatory pattern exhibited alterations in the FEP group. Using oscillatory features improved machine learning performance compared with classical features and FCGR. This study opens up new avenues for exploring the use of CGR in analyzing EEG microstate sequences. Features derived from microstate sequence CGR offer fine-grained neurobiomarkers for psychiatric disorders.

Evaluating the chaos game representation of proteins for applications in machine learning models: prediction of antibody affinity and specificity as a case study

CONTEXT

Machine learning techniques are becoming increasingly important in the selection and optimization of therapeutic molecules, as well as for the selection of formulation components and the prediction of long-term stability. Compared to first-principle models, machine learning techniques are easier to implement, and can identify correlations that would be hard to describe at a mechanistic level, but strongly rely on high-quality input training data. Here, we evaluate the potential of the "chaos game" representation to provide input data for machine learning models. The chaos game is an algorithm originally developed for the production of fractal structures, and later on applied also to the representation of biological sequences, such as genes and proteins. Our results show that the combination of the chaos game representation with convolutional neural networks results in comparable accuracy to other machine learning approaches, thus indicating that chaos game representations could be a valid alternative to existing featurization strategies for machine learning models of biological sequences.

METHODS

We implement the chaos game in Python 3.8.10, and use it to produce fractal as well as novel expanding representations of protein sequences. We then feed the resulting images to a convolutional neural network, built in Python 3.8.10, using TensorFlow 2.9.1, Keras 2.9.0, and the scikit-learn 1.1.1 packages. We select as case study a recently published dataset for the antibody emibetuzumab, with the objective of co-optimizing antibodies variants with both high affinity and low non-specific binding.

SaPt-CNN-LSTM-AR-EA: a hybrid ensemble learning framework for time series-based multivariate DNA sequence prediction

Biological sequence data mining is hot spot in bioinformatics. A biological sequence can be regarded as a set of characters. Time series is similar to biological sequences in terms of both representation and mechanism. Therefore, in the article, biological sequences are represented with time series to obtain biological time sequence (BTS). Hybrid ensemble learning framework (SaPt-CNN-LSTM-AR-EA) for BTS is proposed. Single-sequence and multi-sequence models are respectively constructed with self-adaption pre-training one-dimensional convolutional recurrent neural network and autoregressive fractional integrated moving average fused evolutionary algorithm. In DNA sequence experiments with six viruses, SaPt-CNN-LSTM-AR-EA realized the good overall prediction performance and the prediction accuracy and correlation respectively reached 1.7073 and 0.9186. SaPt-CNN-LSTM-AR-EA was compared with other five benchmark models so as to verify its effectiveness and stability. SaPt-CNN-LSTM-AR-EA increased the average accuracy by about 30%. The framework proposed in this article is significant in biology, biomedicine, and computer science, and can be widely applied in sequence splicing, computational biology, bioinformation, and other fields.

Bioinformatics tools for the sequence complexity estimates

We review current methods and bioinformatics tools for the text complexity estimates (information and entropy measures). The search DNA regions with extreme statistical characteristics such as low complexity regions are important for biophysical models of chromosome function and gene transcription regulation in genome scale. We discuss the complexity profiling for segmentation and delineation of genome sequences, search for genome repeats and transposable elements, and applications to next-generation sequencing reads. We review the complexity methods and new applications fields: analysis of mutation hotspots loci, analysis of short sequencing reads with quality control, and alignment-free genome comparisons. The algorithms implementing various numerical measures of text complexity estimates including combinatorial and linguistic measures have been developed before genome sequencing era. The series of tools to estimate sequence complexity use compression approaches, mainly by modification of Lempel-Ziv compression. Most of the tools are available online providing large-scale service for whole genome analysis. Novel machine learning applications for classification of complete genome sequences also include sequence compression and complexity algorithms. We present comparison of the complexity methods on the different sequence sets, the applications for gene transcription regulatory regions analysis. Furthermore, we discuss approaches and application of sequence complexity for proteins. The complexity measures for amino acid sequences could be calculated by the same entropy and compression-based algorithms. But the functional and evolutionary roles of low complexity regions in protein have specific features differing from DNA. The tools for protein sequence complexity aimed for protein structural constraints. It was shown that low complexity regions in protein sequences are conservative in evolution and have important biological and structural functions. Finally, we summarize recent findings in large scale genome complexity comparison and applications for coronavirus genome analysis.

Zero-shot-capable identification of phage-host relationships with whole-genome sequence representation by contrastive learning

Accurately identifying phage-host relationships from their genome sequences is still challenging, especially for those phages and hosts with less homologous sequences. In this work, focusing on identifying the phage-host relationships at the species and genus level, we propose a contrastive learning based approach to learn whole-genome sequence embeddings that can take account of phage-host interactions (PHIs). Contrastive learning is used to make phages infecting the same hosts close to each other in the new representation space. Specifically, we rephrase whole-genome sequences with frequency chaos game representation (FCGR) and learn latent embeddings that 'encapsulate' phages and host relationships through contrastive learning. The contrastive learning method works well on the imbalanced dataset. Based on the learned embeddings, a proposed pipeline named CL4PHI can predict known hosts and unseen hosts in training. We compare our method with two recently proposed state-of-the-art learning-based methods on their benchmark datasets. The experiment results demonstrate that the proposed method using contrastive learning improves the prediction accuracy on known hosts and demonstrates a zero-shot prediction capability on unseen hosts. In terms of potential applications, the rapid pace of genome sequencing across different species has resulted in a vast amount of whole-genome sequencing data that require efficient computational methods for identifying phage-host interactions. The proposed approach is expected to address this need by efficiently processing whole-genome sequences of phages and prokaryotic hosts and capturing features related to phage-host relationships for genome sequence representation. This approach can be used to accelerate the discovery of phage-host interactions and aid in the development of phage-based therapies for infectious diseases.

PhaVIP: Phage VIrion Protein classification based on chaos game representation and Vision Transformer

MOTIVATION

As viruses that mainly infect bacteria, phages are key players across a wide range of ecosystems. Analyzing phage proteins is indispensable for understanding phages' functions and roles in microbiomes. High-throughput sequencing enables us to obtain phages in different microbiomes with low cost. However, compared to the fast accumulation of newly identified phages, phage protein classification remains difficult. In particular, a fundamental need is to annotate virion proteins, the structural proteins, such as major tail, baseplate, etc. Although there are experimental methods for virion protein identification, they are too expensive or time-consuming, leaving a large number of proteins unclassified. Thus, there is a great demand to develop a computational method for fast and accurate phage virion protein (PVP) classification.

RESULTS

In this work, we adapted the state-of-the-art image classification model, Vision Transformer, to conduct virion protein classification. By encoding protein sequences into unique images using chaos game representation, we can leverage Vision Transformer to learn both local and global features from sequence "images". Our method, PhaVIP, has two main functions: classifying PVP and non-PVP sequences and annotating the types of PVP, such as capsid and tail. We tested PhaVIP on several datasets with increasing difficulty and benchmarked it against alternative tools. The experimental results show that PhaVIP has superior performance. After validating the performance of PhaVIP, we investigated two applications that can use the output of PhaVIP: phage taxonomy classification and phage host prediction. The results showed the benefit of using classified proteins over all proteins.

AVAILABILITY AND IMPLEMENTATION

The web server of PhaVIP is available via: https://phage.ee.cityu.edu.hk/phavip. The source code of PhaVIP is available via: https://github.com/KennthShang/PhaVIP.

Quantification of the Diversity in Gene Structures Using the Principles of Polarization Mapping

Results of computational analysis and visualization of differences in gene structures using polarization coding are presented. A two-dimensional phase screen, where each element of which corresponds to a specific basic nucleotide (adenine, cytosine, guanine, or thymine), displays the analyzed nucleotide sequence. Readout of the screen with a coherent beam characterized by a given polarization state forms a diffracted light field with a local polarization structure that is unique for the analyzed nucleotide sequence. This unique structure is described by spatial distributions of local values of the Stokes vector components. Analysis of these distributions allows the comparison of nucleotide sequences for different strains of pathogenic microorganisms and frequency analysis of the sequences. The possibilities of this polarization-based technique are illustrated by the model data obtained from a comparative analysis of the spike protein gene sequences for three different model variants (Wuhan, Delta, and Omicron) of the SARS-CoV-2 virus. Various modifications of polarization encoding and analysis of gene structures and a possibility for instrumental implementation of the proposed method are discussed.

DNA-Aeon provides flexible arithmetic coding for constraint adherence and error correction in DNA storage

The extensive information capacity of DNA, coupled with decreasing costs for DNA synthesis and sequencing, makes DNA an attractive alternative to traditional data storage. The processes of writing, storing, and reading DNA exhibit specific error profiles and constraints DNA sequences have to adhere to. We present DNA-Aeon, a concatenated coding scheme for DNA data storage. It supports the generation of variable-sized encoded sequences with a user-defined Guanine-Cytosine (GC) content, homopolymer length limitation, and the avoidance of undesired motifs. It further enables users to provide custom codebooks adhering to further constraints. DNA-Aeon can correct substitution errors, insertions, deletions, and the loss of whole DNA strands. Comparisons with other codes show better error-correction capabilities of DNA-Aeon at similar redundancy levels with decreased DNA synthesis costs. In-vitro tests indicate high reliability of DNA-Aeon even in the case of skewed sequencing read distributions and high read-dropout.

KINN: An alignment-free accurate phylogeny reconstruction method based on inner distance distributions of k-mer pairs in biological sequences

Alignment-based methods have faced disadvantages in sequence comparison and phylogeny reconstruction due to their high computational complexity. Alignment-free methods for sequence comparison and phylogeny inference have attracted a great deal of attention in recent years. Here, we explore an alignment-free approach that uses inner distance distributions of k-mer pairs in biological sequences for phylogeny inference. For every sequence in a dataset, our method transforms the sequence into a numeric feature vector consisting of features each representing a specific k-mer pair's contribution to the characterization of the sequentiality uniqueness of the sequence. This newly defined k-mer pair's contribution is an integration of the reverse Kullback-Leibler divergence, pseudo mode and the classic entropy of an inner distance distribution of the k-mer pair in the sequence. Our method has been tested on datasets of complete genome sequences, complete protein sequences, and gene sequences of rRNA of various lengths. Our method achieves the best performance in comparison with state-of-the-art alignment-free methods as measured by the Robinson-Foulds distance between the reference and the constructed phylogeny trees.

Accurate and fast clade assignment via deep learning and frequency chaos game representation

BACKGROUND

Since the beginning of the coronavirus disease 2019 pandemic, there has been an explosion of sequencing of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus, making it the most widely sequenced virus in the history. Several databases and tools have been created to keep track of genome sequences and variants of the virus; most notably, the GISAID platform hosts millions of complete genome sequences, and it is continuously expanding every day. A challenging task is the development of fast and accurate tools that are able to distinguish between the different SARS-CoV-2 variants and assign them to a clade.

RESULTS

In this article, we leverage the frequency chaos game representation (FCGR) and convolutional neural networks (CNNs) to develop an original method that learns how to classify genome sequences that we implement into CouGaR-g, a tool for the clade assignment problem on SARS-CoV-2 sequences. On a testing subset of the GISAID, CouGaR-g achieved an $96.29\%$ overall accuracy, while a similar tool, Covidex, obtained a $77,12\%$ overall accuracy. As far as we know, our method is the first using deep learning and FCGR for intraspecies classification. Furthermore, by using some feature importance methods, CouGaR-g allows to identify k-mers that match SARS-CoV-2 marker variants.

CONCLUSIONS

By combining FCGR and CNNs, we develop a method that achieves a better accuracy than Covidex (which is based on random forest) for clade assignment of SARS-CoV-2 genome sequences, also thanks to our training on a much larger dataset, with comparable running times. Our method implemented in CouGaR-g is able to detect k-mers that capture relevant biological information that distinguishes the clades, known as marker variants.

AVAILABILITY

The trained models can be tested online providing a FASTA file (with 1 or multiple sequences) at https://huggingface.co/spaces/BIASLab/sars-cov-2-classification-fcgr. CouGaR-g is also available at https://github.com/AlgoLab/CouGaR-g under the GPL.

In silico identification of multiple conserved motifs within the control region of Culicidae mitogenomes

Mosquitoes are important vectors for human and animal diseases. Genetic markers, like the mitochondrial COI gene, can facilitate the taxonomic classification of disease vectors, vector-borne disease surveillance, and prevention. Within the control region (CR) of the mitochondrial genome, there exists a highly variable and poorly studied non-coding AT-rich area that contains the origin of replication. Although the CR hypervariable region has been used for species differentiation of some animals, few studies have investigated the mosquito CR. In this study, we analyze the mosquito mitogenome CR sequences from 125 species and 17 genera. We discovered four conserved motifs located 80 to 230 bp upstream of the 12S rRNA gene. Two of these motifs were found within all 392 Anopheles (An.) CR sequences while the other two motifs were identified in all 37 Culex (Cx.) CR sequences. However, only 3 of the 304 non-Culicidae Dipteran mitogenome CR sequences contained these motifs. Interestingly, the short motif found in all 37 Culex sequences had poly-A and poly-T stretch of similar length that is predicted to form a stable hairpin. We show that supervised learning using the frequency chaos game representation of the CR can be used to differentiate mosquito genera from their dipteran relatives.

Multifarious aspects of the chaos game representation and its applications in biological sequence analysis

Chaos game representation (CGR) has been successfully applied in bioinformatics for over 30 years. Since then, many further extensions were announced. Numerical encoding of biological sequences is especially convenient in the visualisation process, free-alignment methods and input preparation for machine learning techniques. The development and applications of CGR have embraced mainly linear nucleotide sequences. However, there were also some attempts to create a representation of proteins. The latter need to be more sophisticated, as arbitrary coordinates for amino acids do not reflect their properties which is crucial during the encoding process. In this paper, the authors summarised various variations of CGRs and their limitations. We began by studying the PROSITE motifs and showed the immense number of amino acid properties employed by different proteins. To this aim, we harnessed the Principal Component Analysis (PCA) and studied the relation between explained variance and the number of features that describe them. It appeared that even after many reductions, about 50 features are non-redundant. This was the reason we introduced an embedding concept from natural language processing which enables adjusting features for a given list of sequences. We presented a simple neural network architecture with one hidden layer and one neuron within it and showed it provides satisfactory results in phylogenetic tree construction in ND5 and SPARC protein cases. To this aim, we transformed CGR representations for all considered sequences using Discrete Fourier Transform (DFT) and applied Unweighted Pair Group Method with Arithmetic Mean (UPGMA) algorithm. Moreover, we indicated some similarities between CGR and Recurrent Neural Networks (RNN). In the end, we attempted to include information about the RNA secondary structure and defined some measures to validate biological significance. We studied their properties and showed on ALMV-3 example its usefulness.

FMG: An observable DNA storage coding method based on frequency matrix game graphs

Using complex biomolecules for storage is a new carbon-based storage method. For example, DNA has the potential to be a good method for archival long-term data storage. Reasonable and efficient coding is the first and most important step in DNA storage. However, current coding methods, such as altruism algorithm, have the problem of low coding efficiency and high complexity, and coding constraints and sets make it difficult to see the coding results visually. In this study, a new DNA storage coding method based on frequency matrix game graph (FMG) is proposed to generate DNA storage coding satisfying combinatorial constraints. Compared with the randomness of the heuristic algorithm that satisfies the constraints, the coding method based on the FMG is deterministic and can clearly explain the coding process. In addition, the constraints and coding results have observable characteristics and are better than the previously published results for the size of the coding set. For example, when length of the code n = 10, hamming distance d = 4, the results obtained by proposed approach combining chaos game and graph are 24% better than the previous results. The proposed coding scheme successfully constructs high-quality coding sets with less complexity, which effectively promotes the development of carbon-based storage coding.

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.