Natural Vector Method Research Articles

The optimal metric for viral genome space

Understanding the structural similarity between genomes is pivotal in classification and phylogenetic analysis. As the number of known genomes rockets, alignment-free methods have gained considerable attention. Among these methods, the natural vector method stands out as it represents sequences as vectors using statistical moments, enabling effective clustering based on families in biological taxonomy. However, determining an optimal metric that combines different elements in natural vectors remains challenging due to the absence of a rigorous theoretical framework for weighting different k-mers and orders. In this study, we address this challenge by transforming the determination of optimal weights into an optimization problem and resolving it through gradient-based techniques. Our experimental results underscore the substantial improvement in classification accuracy achieved by employing these optimal weights, reaching an impressive 92.73% on the testing set, surpassing other alignment-free methods. On one hand, our method offers an outstanding metric for virus classification, and on the other hand, it provides valuable insights into feature integration within alignment-free methods.

Automated recognition of chromosome fusion using an alignment-free natural vector method.

Chromosomal fusion is a significant form of structural variation, but research into algorithms for its identification has been limited. Most existing methods rely on synteny analysis, which necessitates manual annotations and always involves inefficient sequence alignments. In this paper, we present a novel alignment-free algorithm for chromosomal fusion recognition. Our method transforms the problem into a series of assignment problems using natural vectors and efficiently solves them with the Kuhn-Munkres algorithm. When applied to the human/gorilla and swamp buffalo/river buffalo datasets, our algorithm successfully and efficiently identifies chromosomal fusion events. Notably, our approach offers several advantages, including higher processing speeds by eliminating time-consuming alignments and removing the need for manual annotations. By an alignment-free perspective, our algorithm initially considers entire chromosomes instead of fragments to identify chromosomal structural variations, offering substantial potential to advance research in this field.

Geometric analysis of SARS-CoV-2 variants

SARS-CoV-2 as a severe respiratory disease has been prevalent around the world since its first discovery in 2019.As a single-stranded RNA virus, its high mutation rate makes its variants manifold and enables some of them to have high pathogenicity, such as Omicron variant, the most prevalent virus now. Research on the relationship of these SARS-CoV-2 variants, especially exploring their difference is a hot issue. In this study, we constructed a geometric space to represent all SARS-CoV-2 sequences of different variants. An alignment-free method: natural vector method was utilized to establish genome space. The genome space of SARS-CoV-2 was constructed based on the 24-dimensional natural vector and the appropriate metric was determined through performing phylogenetic analysises. Phylogenetic trees of different lineages constructed under the selected natural vector and metric coincided with the lineage naming standards, which means lineages with same alphabetical prefix cluster in phylogenetic trees. Furthermore, the relationships between the various GISAID clades as depicted by the natural graph primarily matched the description provided in the GISAID clade naming.The validity of our geometric space was demonstrated by these phylogenetic analysis results. So in this research, we constructed a geometry space for the genomes of the novel coronavirus SARS-CoV-2, which allows us to compare the different variants. Our geometric space is valuable for resolving the issues insides the virus.

Biochemical Property Based Positional Matrix: A New Approach Towards Genome Sequence Comparison.

The growth of the genome sequence has become one of the emerging areas in the study of bioinformatics. It has led to an excessive demand for researchers to develop advanced methodologies for evolutionary relationships among species. The alignment-free methods have been proved to be more efficient and appropriate related to time and space than existing alignment-based methods for sequence analysis. In this study, a new alignment-free genome sequence comparison technique is proposed based on the biochemical properties of nucleotides. Each genome sequence can be distributed in four parameters to represent a 21-dimensional numerical descriptor using the Positional Matrix. To substantiate the proposed method, phylogenetic trees are constructed on the viral and mammalian datasets by applying the UPGMA/NJ clustering method. Further, the results of this method are compared with the results of the Feature Frequency Profiles method, the Positional Correlation Natural Vector method, the Graph-theoretic method, the Multiple Encoding Vector method, and the Fuzzy Integral Similarity method. In most cases, it is found that the present method produces more accurate results than the prior methods. Also, in the present method, the execution time for computation is comparatively small.

In-depth investigation of the point mutation pattern of HIV-1.

Mutations may produce highly transmissible and damaging HIV variants, which increase the genetic diversity, and pose a challenge to develop vaccines. Therefore, it is of great significance to understand how mutations drive the virulence of HIV. Based on the 11897 reliable genomes of HIV-1 retrieved from HIV sequence Database, we analyze the 12 types of point mutation (A>C, A>G, A>T, C>A, C>G, C>T, G>A, G>C, G>T, T>A, T>C, T>G) from multiple statistical perspectives for the first time. The global/geographical location/subtype/k-mer analysis results report that A>G, G>A, C>T and T>C account for nearly 64% among all SNPs, which suggest that APOBEC-editing and ADAR-editing may play an important role in HIV-1 infectivity. Time analysis shows that most genomes with abnormal mutation numbers comes from African countries. Finally, we use natural vector method to check the k-mer distribution changing patterns in the genome, and find that there is an important substitution pattern between nucleotides A and G, and 2-mer CG may have a significant impact on viral infectivity. This paper provides an insight into the single mutation of HIV-1 by using the latest data in the HIV sequence Database.

Classification of Protein Sequences by a Novel Alignment-Free Method on Bacterial and Virus Families.

The classification of protein sequences provides valuable insights into bioinformatics. Most existing methods are based on sequence alignment algorithms, which become time-consuming as the size of the database increases. Therefore, there is a need to develop an improved method for effectively classifying protein sequences. In this paper, we propose a novel accumulated natural vector method to cluster protein sequences at a lower time cost without reducing accuracy. Our method projects each protein sequence as a point in a 250-dimensional space according to its amino acid distribution. Thus, the biological distance between any two proteins can be easily measured by the Euclidean distance between the corresponding points in the 250-dimensional space. The convex hull analysis and classification perform robustly on virus and bacteria datasets, effectively verifying our method.

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.

Determination of the nucleotide or amino acid composition of genome or protein sequences by using natural vector method and convex hull principle

Although with the continuous development of sequencing technology, the number of genome and protein sequences has grown rapidly, these sequences are only a small part of nature. Biologically, it is still a challenging and important problem to detect and predict some new genome or protein sequences based on real sequence data, which motivates us to solve the problem mathematically. The first step to predict the new sequences is determining the nucleotide or amino acid composition of them. In this paper, we apply natural vector method and convex hull principle to determine the nucleotide or amino acid composition of new genome or protein sequences. Our algorithm is based on optimization strategy. The SARS-CoV-2 genome and protein datasets are used to verify the feasibility of our algorithm. Numerical experiments show that our algorithm can detect and predict possible number of each nucleotide or amino acid of genome and protein sequence with respect to the second order natural vectors.

Analysis of the Genomic Distance Between Bat Coronavirus RaTG13 and SARS-CoV-2 Reveals Multiple Origins of COVID-19.

The severe acute respiratory syndrome COVID-19 was discovered on December 31, 2019 in China. Subsequently, many COVID-19 cases were reported in many other countries. However, some positive COVID-19 samples had been reported earlier than those officially accepted by health authorities in other countries, such as France and Italy. Thus, it is of great importance to determine the place where SARS-CoV-2 was first transmitted to human. To this end, we analyze genomes of SARS-CoV-2 using k-mer natural vector method and compare the similarities of global SARS-CoV-2 genomes by a new natural metric. Because it is commonly accepted that SARS-CoV-2 is originated from bat coronavirus RaTG13, we only need to determine which SARS-CoV-2 genome sequence has the closest distance to bat coronavirus RaTG13 under our natural metric. From our analysis, SARS-CoV-2 most likely has already existed in other countries such as France, India, Netherland, England and United States before the outbreak at Wuhan, China.

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.

A Novel Image Description With the Stretched Natural Vector Method: Application to Face Recognition

Nowadays there is growing research interest in designing high performance algorithms for automatic facial recognition systems, and an efficient computational approach is required. Accurate face recognition, however, is difficult due to facial complexity. In this paper, we propose a novel and efficient facial image representation named the Stretched Natural Vector (SNV) method which is defined on the intensity values in a grayscale image matrix, where each entry in an intensity matrix records the level of gray at a single pixel in a m×n array. We prove that the SNV defined in this context can distinguish photo matrices in strict one-to-one fashion. This is to say it is theoretically possible to fully recover a grayscale image matrix from the corresponding complete SNV. Experiments on a number of datasets demonstrate that our truncated SNV method compares favorably both in recognition accuracy and efficiency (measured in wall-clock time) against “Full-Pixel” algorithm, Principal Component Analysis (PCA) method, and even its widely used variants - two dimensional PCA (2DPCA) method and two dimensional Euler PCA (2D-EPCA) method.

Genome sequence comparison under a new form of tri-nucleotide representation based on bio-chemical properties of nucleotides

Genetic sequence analysis, classification of genome sequence and evolutionary relationship between species using their biological sequences, are the emerging research domain in Bioinformatics. Several methods have already been applied to DNA sequence comparison under tri-nucleotide representation. In this paper, a new form of tri-nucleotide representation is proposed for sequence comparison. The comparison does not depend on the alignment of the sequences. In this representation, the bio-chemical properties of the nucleotides are considered. The novelty of this method is that the sequences of unequal lengths are represented by vectors of the same length and each of the tri-nucleotide formed out of the given sequence has its unique representation. To validate the proposed method, it is verified on several data sets related to mammalians, viruses and bacteria. The results of this method are further compared with those obtained by methods such as probabilistic method, natural vector method, Fourier power spectrum method, multiple encoding vector method, and feature frequency profiles method. Moreover, this method produces accurate phylogeny in all the cases. It is also proved that the time complexity of the present method is less.

Protein Sequence Classification Using Natural Vector and Convex Hull Method.

Protein kinase C (PKC) is a superfamily of enzymes, which regulate numerous cellular responses. The specific function of PKC protein family is mainly governed by its individual protein domains. However, existing protein sequence classification methods based on sequence alignment and sequence analysis models focused little on the domain analysis. In this study, we introduce a novel protein kinase classification method that considers both domain sequence similarity and whole sequence similarity to quantify the evolutionary distance from a specific protein to a protein family. Using the natural vector method, we establish a 60-dimensional space, where each protein is uniquely represented by a vector. We also define a convex hull, consisting of the natural vectors corresponding to all members of a protein family. The sequence similarity between a protein and a protein family, therefore, can be quantified as the distance between the protein vector and the protein family convex hull. We have applied this method in a PKC sample library and the results showed a higher accuracy of classification compared with other alignment-free methods.

A new efficient method for analyzing fungi species using correlations between nucleotides

BackgroundIn recent years, DNA barcoding has become an important tool for biologists to identify species and understand their natural biodiversity. The complexity of barcode data makes it difficult to analyze quickly and effectively. Manual classification of this data cannot keep up to the rate of increase of available data.ResultsIn this study, we propose a new method for DNA barcode classification based on the distribution of nucleotides within the sequence. By adding the covariance of nucleotides to the original natural vector, this augmented 18-dimensional natural vector makes good use of the available information in the DNA sequence. The accurate classification results we obtained demonstrate that this new 18-dimensional natural vector method, together with the random forest classifier algorthm, can serve as a computationally efficient identification tool for DNA barcodes. We performed phylogenetic analysis on the genus Megacollybia to validate our method. We also studied how effective our method was in determining the genetic distance within and between species in our barcoding dataset.ConclusionsThe classification performs well on the fungi barcode dataset with high and robust accuracy. The reasonable phylogenetic trees we obtained further validate our methods. This method is alignment-free and does not depend on any model assumption, and it will become a powerful tool for classification and evolutionary analysis.

Phylogenetic analysis of protein sequences based on a novel k-mer natural vector method

Based on the k-mer model for protein sequence, a novel k-mer natural vector method is proposed to characterize the features of k-mers in a protein sequence, in which the numbers and distributions of k-mers are considered. It is proved that the relationship between a protein sequence and its k-mer natural vector is one-to-one. Phylogenetic analysis of protein sequences therefore can be easily performed without requiring evolutionary models or human intervention. In addition, there exists no a criterion to choose a suitable k, and k has a great influence on obtaining results as well as computational complexity. In this paper, a compound k-mer natural vector is utilized to quantify each protein sequence. The results gotten from phylogenetic analysis on three protein datasets demonstrate that our new method can precisely describe the evolutionary relationships of proteins, and greatly heighten the computing efficiency.

Establishing the phylogeny of Prochlorococcus with a new alignment-free method.

Prochlorococcus marinus, one of the most abundant marine cyanobacteria in the global ocean, is classified into low‐light (LL) and high‐light (HL) adapted ecotypes. These two adapted ecotypes differ in their ecophysiological characteristics, especially whether adapted for growth at high‐light or low‐light intensities. However, some evolutionary relationships of Prochlorococcus phylogeny remain to be resolved, such as whether the strains SS120 and MIT9211 form a monophyletic group. We use the Natural Vector (NV) method to represent the sequence in order to identify the phylogeny of the Prochlorococcus. The natural vector method is alignment free without any model assumptions. This study added the covariances of amino acids in protein sequence to the natural vector method. Based on these new natural vectors, we can compute the Hausdorff distance between the two clades which represents the dissimilarity. This method enables us to systematically analyze both the dataset of ribosomal proteomes and the dataset of 16s‐23s rRNA sequences in order to reconstruct the phylogeny of Prochlorococcus. Furthermore, we apply classification to inspect the relationship of SS120 and MIT9211. From the reconstructed phylogenetic trees and classification results, we may conclude that the SS120 does not cluster with MIT9211. This study demonstrates a new method for performing phylogenetic analysis. The results confirm that these two strains do not form a monophyletic clade in the phylogeny of Prochlorococcus.

Serum amyloid A induces T lymphocyte migration through chemokine receptor CXCR3

Abstract Serum amyloid A (SAA) is a major acute-phase protein with cytokine/chemokine-like properties. It can be expressed at sites of inflammation and induce the migration of immune cells including T lymphocytes to the inflammatory sites. SAA plasma concentration can be 1000 times higher in patients with autoimmune diseases such rheumatoid arthritis, than in healthy people. However, its precise role in inflammation and infection remains unclear. SAA is known to bind to several receptors such as FPRL1, TLR2, and TLR4, etc. It is possible that SAA also use other chemokine receptors to recruit immune cells during the inflammation. In our previous study, we used a mathematical approach called Natural Vector Method (NVM) to analyze the genetic information of all major human chemokines and SAA and found that chemokine receptor CXCR3 may be a new receptor for SAA. We reported here that SAA indeed can induce MAP kinase ERK activation in the CXCR3 over-expressed cell line, and trigger the receptor-mediated intracellular calcium mobilization. Our chemotaxis experiments also showed that SAA promotes CXCR3-overexpressed cell migration. These findings indicate that SAA may use lymphocyte chemokine receptor CXCR3 to recruit activated lymphocytes to the inflammation sites. We will further investigate the signaling pathways involved in the CXCR3 mediated SAA-induced cell migration. We hope that our research work not only helps to understand the function of SAA, but also introduces a new way of finding receptors for the endogenous molecules. [This study is supported by NSF grant DMS-1119612 and NIH grant 1SC3GM098180 awarded to Rong L He]

Ebolavirus classification based on natural vectors.

According to the WHO, ebolaviruses have resulted in 8818 human deaths in West Africa as of January 2015. To better understand the evolutionary relationship of the ebolaviruses and infer virulence from the relationship, we applied the alignment-free natural vector method to classify the newest ebolaviruses. The dataset includes three new Guinea viruses as well as 99 viruses from Sierra Leone. For the viruses of the family of Filoviridae, both genus label classification and species label classification achieve an accuracy rate of 100%. We represented the relationships among Filoviridae viruses by Unweighted Pair Group Method with Arithmetic Mean (UPGMA) phylogenetic trees and found that the filoviruses can be separated well by three genera. We performed the phylogenetic analysis on the relationship among different species of Ebolavirus by their coding-complete genomes and seven viral protein genes (glycoprotein [GP], nucleoprotein [NP], VP24, VP30, VP35, VP40, and RNA polymerase [L]). The topology of the phylogenetic tree by the viral protein VP24 shows consistency with the variations of virulence of ebolaviruses. The result suggests that VP24 be a pharmaceutical target for treating or preventing ebolaviruses.

K-mer natural vector and its application to the phylogenetic analysis of genetic sequences.

Based on the well-known k-mer model, we propose a k-mer natural vector model for representing a genetic sequence based on the numbers and distributions of k-mers in the sequence. We show that there exists a one-to-one correspondence between a genetic sequence and its associated k-mer natural vector. The k-mer natural vector method can be easily and quickly used to perform phylogenetic analysis of genetic sequences without requiring evolutionary models or human intervention. Whole or partial genomes can be handled more effective with our proposed method. It is applied to the phylogenetic analysis of genetic sequences, and the obtaining results fully demonstrate that the k-mer natural vector method is a very powerful tool for analysing and annotating genetic sequences and determining evolutionary relationships both in terms of accuracy and efficiency.

Finding new receptors for serum amyloid A (P6362)

Abstract Serum amyloid A (SAA) is a major acute-phase protein with cytokine/chemokine-like properties. It can be expressed at sites of inflammation and induce the migration of immune cells to the inflammatory sites. SAA plasma concentration can be 1000 times higher in the patients with autoimmune diseases such rheumatoid arthritis, than in the healthy people. However, its precise role in inflammation and infection remains unclear. SAA is known to bind to several receptors such as FPRL1, TLR2, and TLR4, etc. It is possible that SAA also use other chemokine receptors to recruit immune cells during the inflammation. In this study, we used a mathematical approach called Natural Vector Method (NVM) and analyzed the genetic information of all major human chemokines (total 175) and SAA. SAA was found clustered with two chemokines based on both DNA and protein sequences: CXCL9 and CCL23. We hypothesized that SAA may use these chemokines’ receptors, CXCR3 and CCR1. We found that SAA indeed can induce MAP kinase ERK activation in the receptor over-expressed cell line. We will check other receptor-mediated cell functions such as intracellular calcium mobilization, to confirm that SAA can use these two receptors. We hope that our research work not only helps to understand the function of SAA, but also introduces a new way of finding receptors for the endogenous molecules.