Using Huffman coding method to visualize and analyze DNA sequences

On the basis of the Huffman coding method, we propose a new graphical representation of DNA sequence. The representation can avoid degeneracy and loss of information in the transfer of data from a DNA sequence to its graphical representation. Then a multicomponent vector from the representation is introduced to characterize quantitatively DNA sequences. The components of the vector are derived from the graphical representation of DNA primary sequence. The examination of similarities and dissimilarities among the complete coding sequences of β-globin gene of 11 species and six ND6 proteins shows the utility of the scheme.     

A graphical method to construct a phylogenetic tree

A 3D graphical representation of DNA sequences, which has no circuit or degeneracy, is derived for mathematical denotation of DNA sequence. Based on this graphical representation, we propose a new sequence distance measure. We make use of the corresponding similarity matrix to construct a phylogenic tree by virtue of the fuzzy theory. The examination of phylogenic tree belong to eight species illustrates the utility of our approach. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Very efficient search for nucleotide alignments

We describe a very efficient search for nucleotide alignments, which is analogous to the novel very efficient search for protein alignment. Just as it has been the case with the alignment of proteins, based on 20 × 20 adjacency matrices for amino acids, obtained from a superposition of labeled amino acids adjacency matrices for the proteins considered, one can construct labeled matrices of size 4 × 4, listing adjacencies of nucleotides in DNA sequence. The matrix elements correspond to 16 pairs of adjacent nucleotides. To obtain DNA alignments, one combines information in the corresponding matrices for a pair of DNA nucleotides. Matrices are obtained by insertion of the sequential labels for pairs of nucleotides in the corresponding cells of the 4 × 4 tables. When two such matrices are superimposed, one can identify all segments in two DNA sequences, which are shifted relative to one another by the same amount in either direction, without using trial‐and‐error displacements of the two sequences one relative to the other to find local nucleotide alignments. © 2012 Wiley Periodicals, Inc.     

New 2D graphical representation of DNA sequences

We consider a 2D graphical representations of DNA sequences, which avoids loss of information associated with crossing and overlapping of the corresponding curve. We outline an approach, which is based on the construction of a three-component vector whose components are the normalized leading eigenvalues of the L/L matrices associated with DNA. The examination of similarities/dissimilarities among the coding sequences of the first exon of beta-globin gene of different species illustrates the utility of the approach.     

Analysis of similarity/dissimilarity of DNA sequences based on a class of 2D graphical representation

On the basis of a class of 2D graphical representations of DNA sequences, sensitivity analysis has been performed, showing the high-capability of the proposed representations to take into account small modifications of the DNA sequences. And sensitivity analysis also indicates that the absolute differences of the leading eigenvalues of the L/L matrices associated with DNA increase with the increase of the number of the base mutations. Besides, we conclude that the similarity analysis method based on the correlation angles can better eliminate the effects of the lengths of DNA sequences if compared with the method using the Euclidean distances. As application, the examination of similarities/dissimilarities among the coding sequences of the first exon of beta-globin gene of different species has been performed by our method, and the reasonable results verify the validity of our method.     

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.      

Graphical approach to analyzing DNA sequences

Recently, we proposed a 2D graphical representation of DNA sequence [J Comput Chem 25(2004) 1364-1368]. Based on this representation, we outline one approach to search optimal alignment. We also can judge the mutations between bases and an unknown sequence based on its graph and a known sequence's graph.     

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 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.     

RNA–DNA Chimeras in the Context of an RNA World Transition to an RNA/DNA World

The RNA world hypothesis posits that DNA and proteins were later inventions of early life, or the chemistry that gave rise to life. Most scenarios put forth for the emergence of DNA assume a clean separation of RNA and DNA polymer, and a smooth transition between RNA and DNA. However, based on the reality of “clutter” and lack of sophisticated separation/discrimination mechanisms in a protobiological (and/or prebiological) world, heterogeneous RNA–DNA backbone containing chimeric sequences could have been common—and have not been fully considered in models transitioning from an RNA world to an RNA–DNA world. Herein we show that there is a significant decrease in Watson–Crick duplex stability of the heterogeneous backbone chimeric duplexes that would impede base‐pair mediated interactions (and functions). These results point to the difficulties for the transition from one homogeneous system (RNA) to another (RNA/DNA) in an RNA world with a heterogeneous mixture of ribo‐ and deoxyribonucleotides and sequences, while suggesting an alternative scenario of prebiological accumulation and co‐evolution of homogeneous systems (RNA and DNA).     

On the similarity of DNA primary sequences

We consider numerical characterization of graphical representations of DNA primary sequences. In particular we consider graphical representation of DNA of beta-globins of several species, including human, on the basis of the approach of A. Nandy in which nucleic bases are associated with a walk over integral points of a Cartesian x, y-coordinate system. With a so-generated graphical representation of DNA, we associate a distance/distance matrix, the elements of which are given by the quotient of the Euclidean and the graph theoretical distances, that is, through the space and through the bond distances for pairs of bases of graphical representation of DNA. We use eigenvalues of so-constructed matrices to characterize individual DNA sequences. The eigenvalues are used to construct numerical sequences, which are subsequently used for similarity/dissimilarity analysis. The results of such analysis have been compared and combined with similarity tables based on the frequency of occurrence of pairs of bases.     

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.     

Spectral representation of reduced protein models

We consider a spectrum-like two-dimensional graphical representation of proteins based on a reduced protein model in which 20 amino acids are grouped into five classes. This particular grouping of amino acids was suggested by Riddle and co-workers in 1997. The graphical representation is based on depicting sequentially the amino acids on five horizontal lines at equal separations. One-letter codes, B, O, U, X and Y, to which numerical values 1 to 5 have been assigned, are suggested as labels for the fictional amino acids that represent all the amino acids within each group. The approach is illustrated on ND6 proteins of eight species having from 168 to 175 amino acids. While visual inspection of the novel spectral graphical representations of proteins may reveal local similarities and dissimilarities of protein sequences, arithmetic manipulations of spectra offer an elegant route to graphic visualization of the degree of similarity for selected pairs of proteins.     

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     

Visualization of DNA sequences based on 3DD-Curves

In this paper we (1) introduce a new 3D graphical representation of DNA sequences; (2) visualize DNA sequences based on 3DD-Curves; (3) provide a new invariant of DNA sequences based on our 3DD-Curve. All this represents a new development of graphical representation and numerical characterization for DNA sequences.     

A group of 3D graphical representation of DNA sequences based on dual nucleotides

Based on chemical properties of the neighboring dual nucleotides, we reduce a DNA sequence into four 3D graphical representations. Associating with the eigenvalues of the introduced covariance matrix and the introduced measure of similarity, we introduce an approach to make similarity analysis of DNA sequence. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Tunable DNA Origami Motors Translocate Ballistically Over μm Distances at nm/s Speeds

Inspired by biological motor proteins, that efficiently convert chemical fuel to unidirectional motion, there has been considerable interest in developing synthetic analogues. Among the synthetic motors created thus far, DNA motors that undertake discrete steps on RNA tracks have shown the greatest promise. Nonetheless, DNA nanomotors lack intrinsic directionality, are low speed and take a limited number of steps prior to stalling or dissociation. Herein, we report the first example of a highly tunable DNA origami motor that moves linearly over micron distances at an average speed of 40 nm/min. Importantly, nanomotors move unidirectionally without intervention through an external force field or a patterned track. Because DNA origami enables precise testing of nanoscale structure‐function relationships, we were able to experimentally study the role of motor shape, chassis flexibility, leg distribution, and total number of legs in tuning performance. An anisotropic rigid chassis coupled with a high density of legs maximizes nanomotor speed and endurance.     

Cellular automata and its applications in protein bioinformatics

With the explosion of protein sequences generated in the postgenomic era, it is highly desirable to develop high-throughput tools for rapidly and reliably identifying various attributes of uncharacterized proteins based on their sequence information alone. The knowledge thus obtained can help us timely utilize these newly found protein sequences for both basic research and drug discovery. Many bioinformatics tools have been developed by means of machine learning methods. This review is focused on the applications of a new kind of science (cellular automata) in protein bioinformatics. A cellular automaton (CA) is an open, flexible and discrete dynamic model that holds enormous potentials in modeling complex systems, in spite of the simplicity of the model itself. Researchers, scientists and practitioners from different fields have utilized cellular automata for visualizing protein sequences, investigating their evolution processes, and predicting their various attributes. Owing to its impressive power, intuitiveness and relative simplicity, the CA approach has great potential for use as a tool for bioinformatics.