Graphical Bioinformatics

14 2014 Computer program for exact solution to protein alignments 

FIGURE 13.1 Graphical representation of Nandy of the first exon of 3-globin gene of goat (a) and hovine (h). 

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With the development of quantum chemistry and statistical mechanics in the mid-1950s, the chemical graph theory in the mid-1970s, the use of computers in retro-synthesis, and graphical bioinformatics since the year 2000, the characterization of Kant of chemistry as a systematic art or experimental doctrine," although still, in part, true, holds only for parts of chemistry. Just as probabilities and mechanics started to transform parts of physics 100 years ago into mathematical physics, so in more recent times quantum chemistry, statistical mechanics, chemical graph theory, the use of computers in retro-synthesis, and graphical bioinformatics started to transform parts of chemistry into mathmatical chemistry. 

We mentioned the prime nnmbers not only because our first problem in this book relates to prime numbers, but we will later describe some patterns and properties of seqnences of prime numbers, which are one-dimensional mathematical objects (written as sequences of numbers) as two-dimensional objects, illustrated as maps. The same idea has been used already in graphical bioinformatics to represent DNA and protein seqnences as maps [38-41],... 

An alternative graphical representation of DNA as maps is based on the Chaos Game of Barnsley [127], also to be examined more closely later in the book in the section on graphical bioinformatics. In passing, we add that Michael Barnsley is a British mathematician, who got his PhD degree in at the University of Wisconsin, Madison in theoretical chemistry. 

This work can be viewed as a contribution to bioinformatics, not graphical bioinformatics, because it is not based on graphical representations of DNA, but on combinatorics (the combinatorial properties of the prime DNA sequences). So, similarly, the works of Nandy, in which there have been introduced numerical parameters... 

From Table 13.1, it should be clear that the numerical characterizations mentioned in Table 13.1 relate to graphical bioinformatics, to numerical characterizations that facilitate comparative studies of DNA and result in a similarity/dissimilarity table, which is the basis for construction of phylogenetic trees. None of the numerical... 

One of the overlooked contributions that Referee 2 mentioned is the pioneering study in the numerical characterization of DNA, the paper by Raychaudhury and Nandy, Indexing Scheme and Similarity Measures for Macromolecular Sequences [9], We agree that this may be a pioneering study in the numerical qualitative characterization of DNA, but it does not represent the numerical quantitative characterization of DNA, a contribution to solving problems relevant for quantitative graphical bioinformatics. We claim that the first numerical quantitative characterization of DNA is the paper by Randid, Vracko, Nandy, and Basak [4]. 

Let us introduce the amino acid adjacency matrix (AAA matrix) [24] as a tool of graphical bioinformatics. This is a 20 x 20 matrix, the rows and columns of which belong to 20 natural amino acids, which have been ordered as follows ... 

One of the central problems of bioinformatics is DNA and protein alignment, which allows one to arrive at the degree of similarity between different DNA and proteins. Graphical bioinformatics [2,3,6] allows one to arrive at measures of similarity-dissimilarity of DNA and proteins without considering DNA or the protein alignment problem. 

The problem of considerable interest is whether it is possible to recover some lost information accompanying the AAA matrix. Recall how quantitative graphical bioinformatics started by applying the D/D matrix approach developed earlier for characterization of 3-D structures of molecules [12], which was found to be applicable for characterization to 2-D graphical representations of DNA [35]. In doing this, not only that one arrived at a numerical characterization of 2-D graphical representations of DNA, but one was able to recover the lost information due to cancellation of A-G and C-T moves on the x, y coordinate grid. 

Mathematical Treatment of the Axioms of Chemistry To treat. .. by means of axioms, those chemical sciences in which already today mathematics plays an important part in the first rank are quantum chemistry, statistical mechanics, chemical graph theory, and graphical bioinformatics. 

Let us end this book by saying that this book illustrates that the above introductory statement of J. Gasteiger, equally applies to significant parts of this book, if one is to replace chemoinformatics with chemical graph theory, with graphical bioinformatics, and with partial ordering —the three similarly novel disciplines of chemistry that strongly overlap with chemoinformatics and deserve more attention. 

The same explanation applies to the similar comments of Referee 1, who went even further with his statement The paper ignores all seminal developments of 2D methods. Seminal development is development that opens novel directions in research. The paper of Hamory and Ruskin [2] was seminal development that Leong and Morgenthaler [3], Nandy [4], and others followed, which relates to visual, qualitative comparative study of DNA. Indexing of DNA of Nandy et al. was novelty only time will tell how useful it will be and whether it can be characterized as seminal. It certainly is numerical, but it, in our view, neither represents characterization of DNA nor does it lead to matrix characterizations of DNA. If one looks for seminal publication that has led to numerical characterization of DNA, which opened a way to quantitative graphical bioinformatics, then that is the paper of D/D matrices of Randi(5 and coworkers [5]. 

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