RNA Secondary Structure 3D Graphical Representation Without Degeneracy

A 3D graphical representation of RNA secondary structures(3DGRR) has been derived for mathematical denotation of RNA structure. The three-dimensional graphical representation avoids loss of information and resolves structures’ degeneracy. The RNA pseudoknots also can be represented as three-dimensional graphical representations     

RNA secondary structure 2D graphical representation without degeneracy

A two‐dimensional graphical representation (2DGRR) of RNA secondary structures using a two Cartesian coordinates system has been derived for mathematical denotation of RNA structure. The 2DGRR resolves structure degeneracy and avoids loss of information and the limitation that different structures correspond to the same curve. The RNA pseudo‐knots also can be represented as 2D graphical representations. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

On a four-dimensional representation of RNA secondary structures

We propose a 4-D representation of RNA secondary structures. The four-dimensional representation resolves structures’ degeneracy and avoids loss of information and the limitation that different structures correspond the same plot set (or presentation). The RNA pseudoknpts also can be represented as four-dimensional representations. Based on this representation, we outline an approach to compute the similarities between six RNA secondary structures for illustrating the utility of our approach.     

A visual representation for RNA secondary structure and its application

The graphical representation of biological sequences is an important subject in the area of genome studies. We propose a novel visual representation for RNA secondary structures. Some symmetric properties and information on the base distribution and compositions can be intuitively reflected by the projection graphs of the points corresponding to the RNA secondary structures. Then our method is applied to compute the similarity of 12 classical samples and 11 real RNA secondary structures. The results indicate that our method can not only effectively analyze the similarity between RNA secondary structures but also show a high consistency with other literatures. Moreover, our method only needs the geometrical center of the characteristic curve of the RNA secondary structure to compute the similarity matrix, which means a low computational complexity. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Statistical thermodynamics for chain molecules with simple RNA tertiary contacts

A statistical thermodynamic model is developed for chain molecules with simple RNA tertiary contacts. The model, which accounts for the excluded volume effect and the nonadditivity in the free energy, enables reliable predictions for the conformational entropy and partition function for simple tertiary folds. Illustrative applications are made to conformational transitions involving simple tertiary contacts. The model can predict the interplay between the secondary and the tertiary interactions in the conformational changes. Though the present form of the theory is tested and validated in a two-dimensional lattice model, the methodology, which is developed based on a general graphical representation for chain conformations, is applicable to any off-lattice chain representations. Moreover, the analytical formulation of the method makes possible the systematic development of the theory for more complex tertiary structures.     

RNACluster: An integrated tool for RNA secondary structure comparison and clustering

RNA structure comparison is a fundamental problem in structural biology, structural chemistry, and bioinformatics. It can be used for analysis of RNA energy landscapes, conformational switches, and facilitating RNA structure prediction. The purpose of our integrated tool RNACluster is twofold: to provide a platform for computing and comparison of different distances between RNA secondary structures, and to perform cluster identification to derive useful information of RNA structure ensembles, using a minimum spanning tree (MST) based clustering algorithm. RNACluster employs a cluster identification approach based on a MST representation of the RNA ensemble data and currently supports six distance measures between RNA secondary structures. RNACluster provides a user-friendly graphical interface to allow a user to compare different structural distances, analyze the structure ensembles, and visualize predicted structural clusters.     

DB-Curve: a novel 2D method of DNA sequence visualization and representation

The large number of bases in a DNA sequence and the cryptic nature of the 4-alphabet representation make graphical visualization of DNA sequences useful for biologists. However, existing 3D graphical representations are complicated, whereas existing 2D graphical representations suffer from high degeneracy, and many features in a DNA sequence cannot be visualized clearly. This Letter introduces a novel 2D method of DNA representation: the DB-Curve (Dual-Base Curve), which overcomes some of the limitations in existing 2D graphical representations. Many properties of DNA sequences can be observed and visualized easily using a combination of DB-Curves. The new representation can avoid degeneracy completely compared to existing 2D graphical representations of DNA sequences. Unlike 3D graphical representations, no 2D projection is required for the DB-Curve, and this allows for easier analysis of DNA sequences. The DB-Curve provides a useful graphical tool for the visualization and study of DNA sequences.     

Highly compact 2D graphical representation of DNA sequences

Most 2D graphical representations of primary DNA sequences, while offering visual geometrical patterns for depicting sequences, do require considerable space if enough details of such representations are to be visible. In this contribution, we consider a highly compact graphical representation of DNA, which allows visual inspection and numerical characterization of DNA sequences having a large number of nucleic acid bases. The approach is illustrated on the DNA sequences of the first exon of human beta-globin. The same graphical approach not only allows one to depict differences in composition within a single DNA, but makes possible graphical representation of protein sequences, which have hitherto evaded similar 2D visual representations.     

Milestones in graphical bioinformatics

After reviewing the field of graphical bioinformatics, we have selected two dozen of the most significant publications that represent milestones of graphical bioinformatics. These publications can be viewed as forming the backbone of graphical bioinformatics, the branch of bioinformatics that initiates analysis of DNA, RNA, and proteins by considering various graphical representations of these sequences. Graphical bioinformatics, a division of bioinformatics that analyzes sequences of DNA, RNA, proteins, and proteomics maps by developing and using tools of discrete mathematics and graph theory in particular, has expanded since the year 2000, although pioneering contributions date back to Hamory (1983) and Jeffrey (1990). We chronologically follow the development of graphical bioinformatics, without assuming that readers are familiar with discrete mathematics or graph theory. Readers unfamiliar with graph theory may even have some advantage over those who have been only superficially exposed to graph theory, inview of wide misconceptions and misinformation about chemical graph theory among quantum chemists, physical chemists, and medicinal chemists in past decades. © 2013 Wiley Periodicals, Inc.     

Similarity of RNA secondary structures

In this article, we propose a relatively similar measure to compare RNA secondary structures. We first transform an RNA secondary structure into a special sequence representation. Then, on the basis of symbolic sequence complexity, we obtain the relative distance of RNA secondary structures. The examination of similarities/dissimilarities of a set of RNA secondary structures at the 3'-terminus of different viruses illustrates the utility of the approach.     

A semi-supervised learning approach for RNA secondary structure prediction

RNA secondary structure prediction is a key technology in RNA bioinformatics. Most algorithms for RNA secondary structure prediction use probabilistic models, in which the model parameters are trained with reliable RNA secondary structures. Because of the difficulty of determining RNA secondary structures by experimental procedures, such as NMR or X-ray crystal structural analyses, there are still many RNA sequences that could be useful for training whose secondary structures have not been experimentally determined. In this paper, we introduce a novel semi-supervised learning approach for training parameters in a probabilistic model of RNA secondary structures in which we employ not only RNA sequences with annotated secondary structures but also ones with unknown secondary structures. Our model is based on a hybrid of generative (stochastic context-free grammars) and discriminative models (conditional random fields) that has been successfully applied to natural language processing. Computational experiments indicate that the accuracy of secondary structure prediction is improved by incorporating RNA sequences with unknown secondary structures into training. To our knowledge, this is the first study of a semi-supervised learning approach for RNA secondary structure prediction. This technique will be useful when the number of reliable structures is limited.     

Use of statistical measures for analyzing RNA secondary structures

With more and more RNA secondary structures accumulated, the need for comparing different RNA secondary structures often arises in function prediction and evolutionary analysis. Numerous efficient algorithms were developed for comparing different RNA secondary structures, but challenges remain. In this article, a new statistical measure extending the notion of relative entropy based on the proposed stochastic model is evaluated for RNA secondary structures. The results obtained from several experiments on real datasets have shown the effectiveness of the proposed approach. Moreover, the time complexity of our method is favorable by comparing with that of the existing methods which solve the similar problem.     

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.     

The graphical representation of protein sequences based on the physicochemical properties and its applications

Based on the chaos game representation, a 2D graphical representation of protein sequences was introduced in which the 20 amino acids are rearranged in a cyclic order according to their physicochemical properties. The Euclidean distances between the corresponding amino acids from the 2‐D graphical representations are computed to find matching (or conserved) fragments of amino acids between the two proteins. Again, the cumulative distance of the 2D‐graphical representations is defined to compare the similarity of protein. And, the examination of the similarity among sequences of the ND5 proteins of nine species shows the utility of our approach. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Investigations on the secondary structure of 5S-ribonucleic acids by means of pattern recognition

Since the sequence of nucleotides for 5S-ribonucleic acid (5S-RNA) from E. coli was reported in 1967, the secondary structure of this RNA molecule has been discussed. As procaryotic 5S-RNA molecules are functionally identical, they are exchangeable without losing their biological activity, and it is supposed that their secondary structures are also similar. Various workers have concluded that the secondary structure proposed by Fox and Woese is the most likely, although the number of Watson—Crick base-pairs in this structure (24) is less than the number (32) by infrared and nuclear magnetic resonance methods. Application of pattern recognition techniques to Tinoco matrix representations of the secondary structure of 5S-RNA molecules of fifteen different species in all 5S-RNA molecules shows that the helix centre of the Fox—Woese structure is correct. The number of base-pairs can be extended from 25 in this structure up to 29.     

RNA secondary structure alignment based on an extended binary coding method

Recently, we proposed a three‐dimensional cube representation of RNA secondary structure. An efficient method for mutation analysis has been proposed based on the introduced representation. According to the proposed three‐dimensional cube representations, we will introduce an extended binary coding method for RNA secondary structure alignment by converting the structure alignment to sequence alignment. Using our method, the result of structure alignment can be obtained quickly. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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 beta-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.     

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.     

2-D Graphical representation of proteins based on physico-chemical properties of amino acids

A 2-D graphical representation of proteins based on 2-D map of amino acids is outlined. The Amino Acid map was obtained by constructing the partial order on a selected pair of physico-chemical properties of amino acids. The plot of the difference between the (x, y) coordinates of two graphical representations of proteins allows a visual inspection of protein alignment. The approach is illustrated on segments of a protein of the yeast Saccharomyces cerevisiae.