TB-curve, a New 2-D Graphical Representation of DNA Sequences

Based on the classifications of the four nucleic acid bases, we introduce a new 2-D method of DNA representation: TB-curve, which avoids loss of information accompanying alternative 2-D representation in which the curve standing for DNA overlaps and intersects itself. The method is illustrated on the coding sequence of the first exon of human beta-globin gene.     

Letter to the Editor

A new two-dimensional graphical representation of protein sequences is introduced. Twenty concentric evenly spaced circles divided by n radial lines into equal divisions are selected to represent any protein sequence of length n. Each circle represents one of the different 20 amino acids, and each radial line represents a single amino acid of the protein sequence. An efficient numerical method based on the graph is proposed to measure the similarity between two protein sequences. To prove the accuracy of our approach, the method is applied to NADH dehydrogenase subunit 5 (ND5) proteins of nine different species and 24 transferrin sequences from vertebrates. High values of correlation coefficient between our results and the results of ClustalW are obtained (approximately perfect correlations). These values are higher than the values obtained in many other related works.     

A new mapping rule for RNA secondary structures with its applications

According to the characterization of RNA secondary structures, the RNA secondary structures are transformed into elementary sequences, namely characteristic sequences of RNA secondary structures, by representing A, U, G, C in A-U/ G-C pairs, as A′, U′, G′, C′. Based on the representation, three recurrences for mapping RNA secondary structures into 1-D graph, 2-D graph and 3-D graph are given, respectively. Furthermore, a frequency-based method for RNA secondary structures is given in terms of 1-D graph.     

2-D Graphical representation of proteins based on virtual genetic code

We consider a novel 2-D graphical representation of proteins in which individual nucleic acids are represented as “spots” within a square frame distributed according to specific construction rules. The resulting “images” of proteins can not only serve to facilitate visual comparison of similarities and dissimilarities between lengthy protein sequences, but also offer a way for mathematical characterization of protein sequences, analogous to similar considerations for lengthy DNA sequences. Basically the approach is based on the concept of virtual genetic code, which is a hypothetical string of RNA nucleic acid bases, A, C, U and G, which generates reported protein sequences, without the knowledge of the actual genetic code that produces the protein.     

On a four-dimensional representation of DNA primary sequences

We consider a four-dimensional representation of DNA primary sequences by assigning to each of the four basic amino acids A, T, G, C directions along the four orthogonal coordinate axes. Advantages and limitations of the novel representation of DNA primary sequences are discussed, and the use of the 4-D representation is illustrated by constructing novel sequence invariants. Comparisons with the similarity/dissimilarity results based on 2-D and 3-D representations for a set of eight short DNA sequences corresponding to the first exon of beta globin in eight species, including human, are considered to illustrate the use of our novel sequence invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.     

On property of the invariant of graphical representations of DNA sequences

In this article, we consider the influence of variation of DNA sequence on the leading eigenvalue of graphical representation of the biological sequences. The research interpret the rationality of the graphical representation method that compare different DNA sequences. And we show the result on two different models that presented before.      

A novel 2-D graphical representation of DNA sequences of low degeneracy

Some 2-D and 3-D graphical representations of DNA sequences have been given by Nandy, Leong and Mogenthaler, and Randic et al., which give visual characterizations of DNA sequences. In this Letter, we introduce a novel graphical representation of DNA sequences by taking four special vectors in 2-D space to represent the four nucleic acid bases in DNA sequences, so that a DNA sequence is denoted on a plane by a successive vector sequence, which is also a directed walk on the plane. It is showed that the novel graphical representation of DNA sequences has lower degeneracy and less overlapping.     

A naturally logical representation for DNA primary sequences

In this paper, we (1) introduce a logical representation (LR) for DNA primary sequences; (2) show relations between LR and some other representations including the characteristic sequences of a DNA sequence, Randic's 2-D, 4-D representations, and Z-curve (a 3-D graphical representation); and (3) outline the constructions of the S/S matrix specific for a logical sequence and its 2*2 condensed matrix.     

On a 3-D representation of DNA primary sequences

We introduce a graphical representation of DNA primary sequences by taking four special vectors in a 3-D space to represent the four nucleic acid bases in DNA sequences, so that a DNA primary sequence is denoted in a 3-D space by a successive vector sequence which is a directed walk on the space. It is demonstrated that this representation has no overlap and intersection and allows numerical characterization.     

Some notes on 2-D graphical representation of DNA sequence

Some 2-D and 3-D graphical representations of DNA sequences have been given by Nandy, Leong and Mogenthaler, and Randic et al., which give visual characterizations of DNA sequences. In this paper, we presented a novel graphical representation of DNA sequences by taking four special vectors in 2-D Cartesian coordinate system to represent the four nucleic acid bases in DNA sequences, so that a DNA sequence is denoted on a plane by a directed walk. It is shown that the new graphical representation of DNA sequences has lower or nondegeneracy.     

Synthesis of 5′-C- and 2′-O-(Bromoalkyl)-Substituted Ribonucleoside Phosphoramidites for the Post-synthetic Functionalization of Oligonucleotides on Solid Support

The preparation of building blocks for the incorporation of 6′-O-(5-bromopentyl)-substituted β-D -allofuranosylnucleosides and 2′-O-[(3-bromopropoxy)methyl]-substituted ribonucleosides into oligonucleotide sequences is presented (Schemes 1 and 2). These reactive building blocks can be modified with a variety of soft nucleophiles while the (fully protected) sequence is still attached to the solid support. As an example of this strategy, we carried out some preliminary solid-phase substitution and conjugation reactions with DNA sequences containing a 2′-O-[(3-bromopropoxy)methyl]-substituted ribonucleoside (Scheme 3) and determined the pairing properties of duplexes obtained therefrom.     

Anatoliosides: Five Novel Acyclic Monoterpene Glylcosides from Viburnum orientale

Five new acyclic monoterpene glycosides 1 – 5 were isolated from the leaves of Viburnum orientale (Caprifoliaceae). Anatolioside ( 1 ) is a monoterpene diglycoside and its structure was elucidated as linalo-6-yl 2′-O-(α-L -rhamnopyranosyl)β-D -glucopyranoside (arbitrary numbering of linalool moiety). Compounds 2 – 5 are all derivatives of 1 , containing additional monoterpene and sugar units, connected by ester and glycoside bonds. Their structures were established as linalo-6-yl O-[(2E,6R)-6-hydroxy-2, 6-dimethylocta-2,7-dienoyl]-(1? → 4″)-O-α-L -rhamnopyranosyl-(1″? → 2″″)-β-D -glucopyranoside ( = anatolioside A; 2 ), linalo-6-yl O-β-D -glucopyranosyl-(1? → 6?)-O-[(2E,6R)-6-hydroxy-2,6-dimethylocta-2,7-dienoyl]-(1? → 4″)-O-α-L -rhamnopyranosyl-(1″ → 2′)–β-D -glucopyranoside ( = anatolioside B; 3 ), linalo-6-yl O-β-D ribo-hexopyranos-3-ulosyl-(1′? → 6?)-O-[(2E,6R)-6-hydroxy-2,6-dimethylocta-2,7-dienoyl]-(1? → 4″)-O-α-L -rhamnopyranosyl-(1″ → 2′)-β-D -glucopyranoside ( = anatolioside C; 4 ) and linalo-6-yl O-[(2E, 6R)-6-hydroxy-2,6-dimethylocta-2,7-dienoyl]-(1″? → 2″″)-O-β-D -glucopyranosly-(1″″ → 6?)-O-[(2E,6R)-6-hydroxy-2,6-dimethylocta-2,7-dienoyl]-(1? → 4″)-O-α-L -rhamnopyranosyl(1″ → 2′)-β-D -glucopyranoside ( = anatolioside D ; 5 ). The structure determinations were based on spectroscopic and chemical methods (acid and alkaline hydrolysis, acetylation and methylation).     

Computational analyses of mammalian lactate dehydrogenases: Human, mouse, opossum and platypus LDHs

Computational methods were used to predict the amino acid sequences and gene locations for mammalian lactate dehydrogenase (LDH) genes and proteins using genome sequence databanks. Human LDHA, LDHC and LDH6A genes were located in tandem on chromosome 11, while LDH6B and LDH6C genes were on chromosomes 15 and 12, respectively. Opossum LDHC and LDH6B genes were located in tandem with the opossum LDHA gene on chromosome 5 and contained 7 (LDHA and LDHC) or 8 (LDH6B) exons. An amino acid sequence prediction for the opossum LDH6B subunit gave an extended N-terminal sequence, similar to the human and mouse LDH6B sequences, which may support the export of this enzyme into mitochondria. The platypus genome contained at least 3 LDH genes encoding LDHA, LDHB and LDH6B subunits. Phylogenetic studies and sequence analyses indicated that LDHA, LDHB and LDH6B genes are present in all mammalian genomes examined, including a monotreme species (platypus), whereas the LDHC gene may have arisen more recently in marsupial mammals.     

Synthesis of 5-Methyluridine and Its 5′-Mercapto-, 2-Amino-, and 4′,5′-Unsaturated Analogues

The stereospecific cis-hydroxylation of 1-(2,3-dideoxy-β-D -glyceropent-2-enofuranosyl)thymine (1) into 1-β-D -ribofuranosylthymine (2) by osmium tetroxide is described. Treatment of 2′,3′-O, O-isopropylidene-5-methyl-2,5′-anhydrouridine (8) with hydrogen sulfide or methanolic ammonia afforded 5′-deoxy-2′,3′-O, O-isopropylidene-5′-mercapto-5-methyluridine (9) and 2′,3′-O, O-isopropylidene-5-methyl-isocytidine (10) , respectively. The action of ethanolic potassium hydroxide on 5′-deoxy-5′-iodo-2′,3′-O, O-isopropylidene-5-methyluridine (7) gave rise to the corresponding 1-(5-deoxy-β-D -erythropent-4-enofuranosyl)5-methyluracil (13) and 2-O-ethyl-5-methyluridine (14) . The hydrogenation of 2 and its 2′,3′-O, O-isopropylidene derivative 4 over 5% Rh/Al₂O₃ as catalyst generated diastereoisomers of the corresponding 5-methyl-5,6-dihydrouridine ( 17 and 18 ).     

Novel numerical and graphical representation of DNA sequences and proteins

We have introduced novel numerical and graphical representations of DNA, which offer a simple and unique characterization of DNA sequences. The numerical representation of a DNA sequence is given as a sequence of real numbers derived from a unique graphical representation of the standard genetic code. There is no loss of information on the primary structure of a DNA sequence associated with this numerical representation. The novel representations are illustrated with the coding sequences of the first exon of β-globin gene of half a dozen species in addition to human. The method can be extended to proteins as is exemplified by humanin, a 24-aa peptide that has recently been identified as a specific inhibitor of neuronal cell death induced by familial Alzheimer's disease mutant genes.     

On 3-D graphical representation of DNA primary sequences and their numerical characterization

In this article we (1) outline the construction of a 3-D "graphical" representation of DNA primary sequences, illustrated on a portion of the human beta globin gene; (2) describe a particular scheme that transforms the above 3-D spatial representation of DNA into a numerical matrix representation; (3) illustrate construction of matrix invariants for DNA sequences; and (4) suggest a data reduction based on statistical analysis of matrix invariants generated for DNA. Each of the four contributions represents a novel development that we hope will facilitate comparative studies of DNA and open new directions for representation and characterization of DNA primary sequences.     

A 2D graphical representation of DNA sequence based on dual nucleotides and its application

From the perspective of the neighboring dual nucleotides, we introduce a novel 2D graphical representation of DNA sequences based on the magic circle, which correspond to 16 dual nucleotides. So, we can reduce a DNA sequence into a plot set in two‐dimensional space and get a two‐component vector relatively to the introduced covariance matrix. The utility of our approach can be illustrated by the examination of similarities/dissimilarities among the complete coding sequences of β‐globin gene belonging to 11 species. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Analytical irreducible representation bases of the single and double icosahedral groups and their applications

An equivalent basis of icosahedral molecules is introduced in which the basis functions can be transformed under the operations in the icosahedral group (I_h). In this equivalent basis, the irreducible representation basis (IRB) of I_h, including the double‐valued IRB of I, is deduced analytically based on the method introduced in the literature [J. Comput. Chem. 17 , 851 (1996)]. Therefore the concepts of symmetry‐matrix and symmetry‐supermatrix can be used in the single‐ and multiconfiguration self‐consistent field methods (including relativistic effects) to reduce the storage of two‐electron integrals and calculations of Fock matrix during iterations by a factor of ca. 10,000. In addition, the equivalent basis of I_h can also be used to reduce the calculations of atoms and representations of rank ≥ 2 tensors. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 615–624, 2000     

Three‐unit semicircles curve: A compact 3D graphical representation of DNA sequences based on classifications of nucleotides

A new three‐dimensional graphical representation of DNA sequences, three‐unit semicircles (TUS)‐curve, which maps a given sequence into a dot sequences embedded in three‐unit semicircles, is proposed based on three biclassifications of nucleotides. TUS‐curve has the merit of compactness and could avoid the degeneracy and loss of information. The geometrical center of the curve, which indicates the distribution of base frequencies of the corresponding DNA sequence, is extracted and applied to analyze the similarity of various species. Phylogenetic tree of 11 species based on their first exons of β‐globin genes showed that the TUS‐curve is a powerful tool to get valuable biological information. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011