Proper distance metrics for phylogenetic analysis using complete genomes without sequence alignment

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.

An Information-Entropy Position-Weighted K-Mer Relative Measure for Whole Genome Phylogeny Reconstruction

Alignment methods have faced disadvantages in sequence comparison and phylogeny reconstruction due to their high computational costs in handling time and space complexity. On the other hand, alignment-free methods incur low computational costs and have recently gained popularity in the field of bioinformatics. Here we propose a new alignment-free method for phylogenetic tree reconstruction based on whole genome sequences. A key component is a measure called information-entropy position-weighted k-mer relative measure (IEPWRMkmer), which combines the position-weighted measure of k-mers proposed by our group and the information entropy of frequency of k-mers. The Manhattan distance is used to calculate the pairwise distance between species. Finally, we use the Neighbor-Joining method to construct the phylogenetic tree. To evaluate the performance of this method, we perform phylogenetic analysis on two datasets used by other researchers. The results demonstrate that the IEPWRMkmer method is efficient and reliable. The source codes of our method are provided at https://github.com/ wuyaoqun37/IEPWRMkmer.

A fast alignment-free bioinformatics procedure to infer accurate distance-based phylogenetic trees from genome assemblies

This paper describes a novel alignment-free distance-based procedure for inferring phylogenetic trees from genome contig sequences using publicly available bioinformatics tools. For each pair of genomes, a dissimilarity measure is first computed and next transformed to obtain an estimation of the number of substitution events that have occurred during their evolution. These pairwise evolutionary distances are then used to infer a phylogenetic tree and assess a confidence support for each internal branch. Analyses of both simulated and real genome datasets show that this bioinformatics procedure allows accurate phylogenetic trees to be reconstructed with fast running times, especially when launched on multiple threads. Implemented in a publicly available script, named JolyTree, this procedure is a useful approach for quickly inferring species trees without the burden and potential biases of multiple sequence alignments.

Virus classification in 60-dimensional protein space

Due to vast sequence divergence among different viral groups, sequence alignment is not directly applicable to genome-wide comparative analysis of viruses. More and more attention has been paid to alignment-free methods for whole genome comparison and phylogenetic tree reconstruction. Among alignment-free methods, the recently proposed "Natural Vector (NV) representation" has successfully been used to study the phylogeny of multi-segmented viruses based on a 12-dimensional genome space derived from the nucleotide sequence structure. But the preference of proteomes over genomes for the determination of viral phylogeny was not deeply investigated. As the translated products of genes, proteins directly form the shape of viral structure and are vital for all metabolic pathways. In this study, using the NV representation of a protein sequence along with the Hausdorff distance suitable to compare point sets, we construct a 60-dimensional protein space to analyze the evolutionary relationships of 4021 viruses by whole-proteomes in the current NCBI Reference Sequence Database (RefSeq). We also take advantage of the previously developed natural graphical representation to recover viral phylogeny. Our results demonstrate that the proposed method is efficient and accurate for classifying viruses. The accuracy rates of our predictions such as for Baltimore II viruses are as high as 95.9% for family labels, 95.7% for subfamily labels and 96.5% for genus labels. Finally, we discover that proteomes lead to better viral classification when reliable protein sequences are abundant. In other cases, the accuracy rates using proteomes are still comparable to that of genomes.

Whole genome/proteome based phylogeny reconstruction for prokaryotes using higher order Markov model and chaos game representation

Traditional methods for sequence comparison and phylogeny reconstruction rely on pair wise and multiple sequence alignments. But alignment could not be directly applied to whole genome/proteome comparison and phylogenomic studies due to their high computational complexity. Hence alignment-free methods became popular in recent years. Here we propose a fast alignment-free method for whole genome/proteome comparison and phylogeny reconstruction using higher order Markov model and chaos game representation. In the present method, we use the transition matrices of higher order Markov models to characterize amino acid or DNA sequences for their comparison. The order of the Markov model is uniquely identified by maximizing the average Shannon entropy of conditional probability distributions. Using one-dimensional chaos game representation and linked list, this method can reduce large memory and time consumption which is due to the large-scale conditional probability distributions. To illustrate the effectiveness of our method, we employ it for fast phylogeny reconstruction based on genome/proteome sequences of two species data sets used in previous published papers. Our results demonstrate that the present method is useful and efficient.

AVAILABILITY AND IMPLEMENTATION

The source codes for our algorithm to get the distance matrix and genome/proteome sequences can be downloaded from ftp://121.199.20.25/. The software Phylip and EvolView we used to construct phylogenetic trees can be referred from their websites.

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

Background

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

Results

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

Conclusion

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

Whole-proteome based phylogenetic tree construction with inter-amino-acid distances and the conditional geometric distribution profiles

There has been a growing interest in alignment-free methods for whole genome comparison and phylogenomic studies. In this study, we propose an alignment-free method for phylogenetic tree construction using whole-proteome sequences. Based on the inter-amino-acid distances, we first convert the whole-proteome sequences into inter-amino-acid distance vectors, which are called observed inter-amino-acid distance profiles. Then, we propose to use conditional geometric distribution profiles (the distributions of sequences where the amino acids are placed randomly and independently) as the reference distribution profiles. Last the relative deviation between the observed and reference distribution profiles is used to define a simple metric that reflects the phylogenetic relationships between whole-proteome sequences of different organisms. We name our method inter-amino-acid distances and conditional geometric distribution profiles (IAGDP). We evaluate our method on two data sets: the benchmark dataset including 29 genomes used in previous published papers, and another one including 67 mammal genomes. Our results demonstrate that the new method is useful and efficient.

Measurement of word frequencies in genomic DNA sequences based on partial alignment and fuzzy set

Accompanied with the rapid increase of the amount of data registered in the databases of biological sequences, the need for a fast method of sequence comparison applicable to sequences of large size is also increasing. In general, alignment is used for sequence comparison. However, the alignment may not be appropriate for comparison of sequences of large size such as whole genome sequences due to its large time complexity. In this article, we propose a semi alignment-free method of sequence comparison based on word frequency distributions, in which we partially use the alignment to measure word frequencies along with the idea of fuzzy set theory. Experiments with ten bacterial genome sequences demonstrated that the fuzzy measurements has the effect that facilitates discrimination between close relatives and distant relatives.

Analyzing multi-locus plant barcoding datasets with a composition vector method based on adjustable weighted distance

BACKGROUND

The composition vector (CV) method has been proved to be a reliable and fast alignment-free method to analyze large COI barcoding data. In this study, we modify this method for analyzing multi-gene datasets for plant DNA barcoding. The modified method includes an adjustable-weighted algorithm for the vector distance according to the ratio in sequence length of the candidate genes for each pair of taxa.

METHODOLOGY/PRINCIPAL FINDINGS

Three datasets, matK+rbcL dataset with 2,083 sequences, matK+rbcL dataset with 397 sequences and matK+rbcL+trnH-psbA dataset with 397 sequences, were tested. We showed that the success rates of grouping sequences at the genus/species level based on this modified CV approach are always higher than those based on the traditional K2P/NJ method. For the matK+rbcL datasets, the modified CV approach outperformed the K2P-NJ approach by 7.9% in both the 2,083-sequence and 397-sequence datasets, and for the matK+rbcL+trnH-psbA dataset, the CV approach outperformed the traditional approach by 16.7%.

CONCLUSIONS

We conclude that the modified CV approach is an efficient method for analyzing large multi-gene datasets for plant DNA barcoding. Source code, implemented in C++ and supported on MS Windows, is freely available for download at http://math.xtu.edu.cn/myphp/math/research/source/Barcode_source_codes.zip.

Composition vector method based on maximum entropy principle for sequence comparison

The composition vector (CV) method is an alignment-free method for sequence comparison. Because of its simplicity when compared with multiple sequence alignment methods, the method has been widely discussed lately; and some formulas based on probabilistic models, like Hao’s and Yu’s formulas, have been proposed. In this paper, we improve these formulas by using the entropy principle which can quantify the nonrandomness occurrence of patterns in the sequences. More precisely, existing formulas are used to generate a set of possible formulas from which we choose the one that maximizes the entropy. We give the closed-form solution to the resulting optimization problem. Hence, from any given CV formula, we can find the corresponding one that maximizes the entropy. In particular, we show that Hao’s formula is itself maximizing the entropy and we derive a new entropy-maximizing formula from Yu’s formula. We illustrate the accuracy of our new formula by using both simulated and experimental data sets. For the simulated data sets, our new formula gives the best consensus and significant values for three different kinds of evolution models. For the data set of tetrapod 18S rRNA sequences, our new formula groups the clades of bird and reptile together correctly, where Hao’s and Yu’s formulas failed. Using real data sets with different sizes, we show that our formula is more accurate than Hao’s and Yu’s formulas even for small data sets.

A visualization of 3D proteome universe: mapping of a proteome ensemble into 3D space based on the protein-structure composition

To visualize a bird's-eye view of an ensemble of proteomes for various species, we recently developed a novel method of mapping a proteome ensemble into Three-Dimensional (3D) vector space. In this study, the "proteome" is defined as the entire set of all proteins encoded in a genome sequence, and these proteins were dealt with at the level of the SCOP Fold. First, we represented the proteome of a species s by a 1053-dimensional vector x(s), where its length ∣x(s)∣ represents the overall amount of all the SCOP Folds in the proteome, and its unit vector x(s)/∣x(s)∣ represents the relative composition of the SCOP Folds in the proteome and the size of the dimension, 1053, is the number of all possible Folds in the proteome ensemble given. Second, we mapped the vector x(s) to the 3D vector y(s), based on the two simple principles: (1) ∣y(s)∣=∣x(s)∣, and (2) the angle between y(s) and y(t) maximally correlates with the angle between x(s) and x(t). We applied to the mapping of a proteome ensemble for 456 species, which were retrieved from the Genomes TO Protein structures and functions (GTOP) database. As a result, we succeeded in the mapping in that the properties of the 1053-dimensional vectors were quantitatively conserved in the 3D vectors. Particularly, the angles between vectors before and after the mapping highly correlated with each other (correlation coefficients were 0.95-0.96). This new mapping method will allow researchers to intuitively interpret the visual information presented in the maps in a highly effective manner.

A mathematical consideration of the word-composition vector method in comparison of biological sequences

To measure the similarity or dissimilarity between two given biological sequences, several papers proposed metrics based on the "word-composition vector". The essence of these metrics is as follows. First, we count the appearance frequencies of all the K-tuple words throughout each of two given sequences. Then, the two given sequences are transformed into their respective word-composition vectors. Next, the distance metrics, for example the angle between the two vectors, are calculated. A significant issue is to determine the optimal word size K. With a mathematical model of mutational events (including substitutions, insertions, deletions and duplications) that occur in sequences, we analyzed how the angle between the composition vectors depends on the mutational events. We also considered the optimal word size (=resolution) from our original approach. Our results were verified by computational experiments using artificially generated sequences, amino acid sequences of hemoglobin and nucleotide sequences of 16S ribosomal RNA.

Whole-proteome phylogeny of large dsDNA viruses and parvoviruses through a composition vector method related to dynamical language model

BACKGROUND

The vast sequence divergence among different virus groups has presented a great challenge to alignment-based analysis of virus phylogeny. Due to the problems caused by the uncertainty in alignment, existing tools for phylogenetic analysis based on multiple alignment could not be directly applied to the whole-genome comparison and phylogenomic studies of viruses. There has been a growing interest in alignment-free methods for phylogenetic analysis using complete genome data. Among the alignment-free methods, a dynamical language (DL) method proposed by our group has successfully been applied to the phylogenetic analysis of bacteria and chloroplast genomes.

RESULTS

In this paper, the DL method is used to analyze the whole-proteome phylogeny of 124 large dsDNA viruses and 30 parvoviruses, two data sets with large difference in genome size. The trees from our analyses are in good agreement to the latest classification of large dsDNA viruses and parvoviruses by the International Committee on Taxonomy of Viruses (ICTV).

CONCLUSIONS

The present method provides a new way for recovering the phylogeny of large dsDNA viruses and parvoviruses, and also some insights on the affiliation of a number of unclassified viruses. In comparison, some alignment-free methods such as the CV Tree method can be used for recovering the phylogeny of large dsDNA viruses, but they are not suitable for resolving the phylogeny of parvoviruses with a much smaller genome size.