Classification Maps: A New Mathematical Tool Supporting the Diagnosis of Age-Related Macular Degeneration.

OBJECTIVE: A new diagnostic graphical tool-classification maps-supporting the detection of Age-Related Macular Degeneration (AMD) has been constructed. METHODS: The classification maps are constructed using the ordinal regression model. In the ordinal regression model, the ordinal variable (the dependent variable) is the degree of the advancement of AMD. The other variables, such as CRT (Central Retinal Thickness), GCC (Ganglion Cell Complex), MPOD (Macular Pigment Optical Density), ETDRS (Early Treatment Diabetic Retinopathy Study), Snellen and Age have also been used in the analysis and are represented on the axes of the maps. RESULTS: Here, 132 eyes were examined and classified to the AMD advancement level according to the four-point Age-Related Eye Disease Scale (AREDS): AREDS 1, AREDS 2, AREDS 3 and AREDS 4. These data were used for the creation of two-dimensional classification maps for each of the four stages of AMD. CONCLUSIONS: The maps allow us to perform the classification of the patient's eyes to particular stages of AMD. The pairs of the variables represented on the axes of the maps can be treated as diagnostic identifiers necessary for the classification to particular stages of AMD.

4D-Dynamic Representation of DNA/RNA Sequences: Studies on Genetic Diversity of Echinococcus multilocularis in Red Foxes in Poland.

The 4D-Dynamic Representation of DNA/RNA Sequences, an alignment-free bioinformatics method recently developed by us, has been used to study the genetic diversity of Echinococcus multilocularis in red foxes in Poland. Sequences of three mitochondrial genes, i.e., NADH dehydrogenase subunit 2 (nad2), cytochrome b (cob), and cytochrome c oxidase subunit 1 (cox1), are analyzed. The sequences are represented by sets of material points in a 4D space, i.e., 4D-dynamic graphs. As a visualization of the sequences, projections of the graphs into 3D space are shown. The differences between 3D graphs corresponding to European, Asian, and American haplotypes are small. Numerical characteristics (sequence descriptors) applied in the studies can recognize the differences. The concept of creating descriptors of 4D-dynamic graphs has been borrowed from classical dynamics; these are coordinates of the centers or mass and moments of inertia of 4D-dynamic graphs. Based on these descriptors, classification maps are constructed. The concentrations of points in the maps indicate one Polish haplotype (EmPL9) of Asian origin.

Applications of 2D and 3D-Dynamic Representations of DNA/RNA Sequences for a Description of Genome Sequences of Viruses.

The aim of the studies is to show that graphical bioinformatics methods are good tools for the description of genome sequences of viruses. A new approach to the identification of unknown virus strains, is proposed. METHODS: Biological sequences have been represented graphically through 2D and 3D-Dynamic Representations of DNA/RNA Sequences - theoretical methods for the graphical representation of the sequences developed by us previously. In these approaches, some ideas of the classical dynamics have been introduced to bioinformatics. The sequences are represented by sets of material points in 2D or 3D spaces. The distribution of the points in space is characteristic of the sequence. The numerical parameters (descriptors) characterizing the sequences correspond to the quantities typical of classical dynamics. RESULTS: Some applications of the theoretical methods have been briefly reviewed. 2D-dynamic graphs representing the complete genome sequences of SARS-CoV-2 are shown. CONCLUSION: It is proved that the 3D-Dynamic Representation of DNA/RNA Sequences, coupled with the random forest algorithm, classifies successfully the subtypes of influenza A virus strains.

Non-standard bioinformatics characterization of SARS-CoV-2.

A non-standard bioinformatics method, 4D-Dynamic Representation of DNA/RNA Sequences, aiming at an analysis of the information available in nucleotide databases, has been formulated. The sequences are represented by sets of "material points" in a 4D space - 4D-dynamic graphs. The graphs representing the sequences are treated as "rigid bodies" and characterized by values analogous to the ones used in the classical dynamics. As the graphical representations of the sequences, the projections of the graphs into 2D and 3D spaces are used. The method has been applied to an analysis of the complete genome sequences of the 2019 novel coronavirus. As a result, 2D and 3D classification maps are obtained. The coordinate axes in the maps correspond to the values derived from the exact formulas characterizing the graphs: the coordinates of the centers of mass and the 4D moments of inertia. The points in the maps represent sequences and their coordinates are used as the classifiers. The main result of this work has been derived from the 3D classification maps. The distribution of clusters of points which emerged in these maps, supports the hypothesis that SARS-CoV-2 may have originated in bat and in pangolin. Pilot calculations for Zika virus sequence data prove that the proposed approach is also applicable to a description of time evolution of genome sequences of viruses.

Spectral-dynamic representation of DNA sequences.

A graphical representation of DNA sequences in which the distribution of a particular base B=A,C,G,T is represented by a set of discrete lines has been formulated. The methodology of this approach has been borrowed from two areas of physics: spectroscopy and dynamics. Consequently, the set of discrete lines is referred to as the B-spectrum. Next, the B-spectrum is transformed to a rigid body composed of material points. In this way a dynamic representation of the DNA sequence has been obtained. The centers of mass of these rigid bodies, divided by their moments of inertia, have been taken as the descriptors of the spectra and, thus, of the DNA sequences. The performance of this method on a standard set of data commonly applied by authors introducing new approaches to bioinformatics (the first exons of ß-globin genes of different species) proved to be very good.

Characterizing the Zika Virus Genome - A Bioinformatics Study.

BACKGROUND: The recent epidemic of Zika virus infections in South and Latin America have raised serious concern on its ramifications for the population in the Americas and spread of the virus worldwide. The Zika virus disease is a relatively new phenomenon for which sufficient and comprehensive data and investigative reports have not been available to date. OBJECTIVE: To carry out a bioinformatics study of the available Zika virus genomic sequences to characterize the virus. METHOD: 2D graphical representation method is used for visual rendering and compute sequence parameters and descriptors of the African and Asian-American groups of the Zika viruses to characterize the sequences. We also used MEGA5.2 and other software to compute various biological properties of interest like phylogenetic relationships, transition-transversion ratios, amino acid usage, codon usage bias and hydropathy index of the Zika genomes and virions. RESULTS: The phylogenetic relationships show that the African and Asian-American Zika virus genomes are grouped in two clades. The 2D plots of typical genomes of these types also show dramatic differences indicating that the gene sequences at the 5'-end coding regions for the structural proteins are rather strongly conserved. Among other characteristics, the transition/transversion ratio matrices for the sequences in each of the two clades show that analogous to the dengue virus, the transition rates are about 10 to 15 times the transversion rates. CONCLUSION: These findings are important for computer-assisted approaches towards surveillance of emerging Zika virus strains as well as in the design of drugs and vaccines to combat the growth and spread of the Zika virus.

20D-dynamic representation of protein sequences.

A new method of comparison of protein sequences has been formulated. The sequence of amino acids is represented by a set of point masses in a 20D space. The distribution of points in the space is obtained by applying the method of a walk in the 20D space. Projections of the 20D representation into 2D or 3D spaces illustrate the distribution of particular amino acids along the sequence. 20D moments of inertia are proposed as new descriptors of protein sequences.

Non-standard similarity/dissimilarity analysis of DNA sequences.

Similarity/dissimilarity analysis of DNA sequences is performed using 3D-dynamic representation. The sequences are represented by material points in a 3D-space. Descriptors related to such 3D-dynamic graphs are calculated. A new normalized similarity measure is introduced for a comparison of the sequences. The method is applied to ß-globin (HBB) genes of different species. Different methods are compared. The multidimensionality of similarity space of complex objects is discussed (different results for each of the methods). It is also shown that it is easier to find the properties which are consistent with the observation of the evolution of the species for the second exons of ß-globin gene rather than for the first ones.

3D-dynamic representation of DNA sequences.

A new 3D graphical representation of DNA sequences is introduced. This representation is called 3D-dynamic representation. It is a generalization of the 2D-dynamic dynamic representation. The sequences are represented by sets of "material points" in the 3D space. The resulting 3D-dynamic graphs are treated as rigid bodies. The descriptors characterizing the graphs are analogous to the ones used in the classical dynamics. The classification diagrams derived from this representation are presented and discussed. Due to the third dimension, "the history of the graph" can be recognized graphically because the 3D-dynamic graph does not overlap with itself. Specific parts of the graphs correspond to specific parts of the sequence. This feature is essential for graphical comparisons of the sequences. Numerically, both 2D and 3D approaches are of high quality. In particular, a difference in a single base between two sequences can be identified and correctly described (one can identify which base) by both 2D and 3D methods.

Descriptors of 2D-dynamic graphs as a classification tool of DNA sequences.

A new tool of the classification of DNA sequences is introduced. The method is based on 2D-dynamic graphs and their descriptors. Using the descriptors created by centers of masses, moments of inertia, angles between the x axis and the principal axis of inertia of the 2D-dynamic graphs one can obtain classification diagrams in which similar sequences are clustered in separated areas.

Graphical and numerical representations of DNA sequences: statistical aspects of similarity.

New approaches aiming at a detailed similarity/dissimilarity analysis of DNA sequences are formulated. Several corrections that enrich the information which may be derived from the alignment methods are proposed. The corrections take into account the distributions along the sequences of the aligned bases (neglected in the standard alignment methods). As a consequence, different aspects of similarity, as for example asymmetry of the gene structure, may be studied either using new similarity measures associated with four-component spectral representation of the DNA sequences or using alignment methods with corrections introduced in this paper. The corrections to the alignment methods and the statistical distribution moment-based descriptors derived from the four-component spectral representation of the DNA sequences are applied to similarity/dissimilarity studies of ß-globin gene across species. The studies are supplemented by detailed similarity studies for histones H1 and H4 coding sequences. The data are described according to the latest version of the EMBL database. The work is supplemented by a concise review of the state-of-art graphical representations of DNA sequences.

Classification studies based on a spectral representation of DNA.

The aim of this paper is to provide a new tool to classify the nucleic acid sequences. The profiles based on the values characterizing DNA sequences (descriptors derived from recently introduced graphical representation) are used as a basis of classification schemes related to different aspects of similarity of the sequences. New multicomponent similarity measures based on these descriptors have been defined. Each component of the new measures can be analyzed separately. The new measures are consistent with the standard ones but they contain more detailed information. In particular, it has been shown that within the new approach one can define a quantity which converges to the standard similarity measure. An application of the multicomponent similarity measure to families of histone sequences demonstrates the power and efficiency of the method.