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 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.     

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.     

Use of atom codes for the classification of chemical shifts of benzenoid hydrocarbons

Atomic codes which enumerate the first, second, third, etc., nearest neighbors are considered as the basis of a systematic search for regularities in available molecular data. Specifically, benzenoid conjugated hydrocarbons are considered and proton chemical shifts are reviewed in an effort to detect trends among the observed values and features characterizing the atomic environment.     

Higher-order Fibonacci numbers

We consider a generalization of Fibonacci numbers that was motivated by the relationship of the HosoyaZ topological index to the Fibonacci numbers. In the case of the linear chain structures the new higher order Fibonacci numbers ^h F _n are directly related to the higher order Hosoya-typeZ numbers. We investigate the limitsF _n /F _n–1 and the corresponding equations, the roots of which allow one to write a general expression for^hF_n. We also report on the ^h F counting polynomials that give the partition of the ^h F numbers in contributions arising fromk pairs of disjoint paths of lengthh. It is interesting to see that the partitions of ^h F are hidden in the Pascal triangle in a similar way to the partitions of the Fibonacci numbers that were discovered some time ago by Hoggatt. We end with illustrations of the recursion formulas for the higher order Hosoya numbers for several families of graphs that are based on the corresponding recursions for the higher Fibonacci numbers.Dedicated to Professor Haruo Hosoya of Ochanomizu University, Tokyo, Japan, on the occasion of 25 years of the topological index Z.     

Condensed representation of DNA primary sequences

With rapid reporting of DNA sequences derived from automated DNA sequencing techniques, the problem of reviewing and ordering such information has become acute. We have introduced a condensed representation of primary sequences of DNA that offers an alternative method of registering DNA. The advantage of the condensed codes for DNA is that it not only offers fast, qualitative comparisons of DNA but also allows quantitative comparisons of DNA from different sources. The approach is outlined for a particular human beta globin sequence extract. Using the condensed representation of the primary DNA sequences, comparisons are made between primary sequences for Exon 1 of human beta globin and seven other beta globins.     

Hybridization in methylenecyclopropane and related molecules having exocyclic double bonds

The hybridization in methylenecyolopropane, dimethylenecyclopropane, bisethanoallene, and related molecules containing double bonds externally attached to a cyclopropane ring is considered by applying the method of maximum overlap. The results show that the bond overlap of an exocyclic double bond is larger than the bond overlap of a normal C=C bond, and double bonds in allenes have even larger overlap than an exocyclic C=C bond. The results of the calculations are correlated with some available experimental data.     

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.     

In vivo REPAIR OF CYTOSINE HYDRATES IN DNA OF CULTURED HUMAN LYMPHOBLASTS

Abstract— Ultraviolet irradiation of DNA in vitro results in the production of a wide variety of pyrimidine base alterations, including cytosine hydrates. Enzymes that initiate the repair of monomeric pyrimidine damage have been identified in both bacterial and mammalian systems; however, the in vivo formation and repair of cytosine photohydrates has not been demonstrated in cellular DNA. Using Escherichia coli endonuclease III as a damage-specific probe, we have shown that ring-saturated pyrimidines are formed in cultured human cells by irradiation with broadspectrum UV light. In addition, these types of base damage are removed from the DNA of human lymphoblasts within 5 h following the irradiation. Analysis of the action spectrum for the formation of cytosine hydrates in DNA reveals that these photoproducts are formed most efficiently by irradiation in the range of 255–265 nm light, coinciding with the wavelengths that are maximally absorbed by the DNA bases.