On the Existence of Wavelet Symmetries in Archaea DNA

Abstract

This paper deals with the complex unit roots representation of archea DNA sequences and the analysis of symmetries in the wavelet coefficients of the digitalized sequence. It is shown that even for extremophile archaea, the distribution of nucleotides has to fulfill some (mathematical) constraints in such a way that the wavelet coefficients are symmetrically distributed, with respect to the nucleotides distribution.

On the fractal analysis of gene sequences involved in atherosclerosis by binary image indicator matrix

“…In this paper, the BIIM was used to convert uni-dimensional symbolic sequences (such as DNA sequences) in 2-D images and to compute the FD and lacunarity. This method allows to visualize a typical patterns of nucleotide that looks like a fractal arrangement such as demonstrated by Cattani in recent works and in the study of complexity of Caenorhabditis elegans [2,19,[24][25][26].…”

Information Entropy As a Basic Building Block of Complexity Theory

“…To understand this aspect better, we may take the case of estimating information entropy from DNA sequences as a concrete example. While entropy is close to two bits, based on the distribution of nucleotide bases [14], it becomes significantly lower than two bits when sequential correlations are taken into account [69] (for recent studies on DNA sequences, we refer to [70][71][72][73][74][75]). …”

Uncertainty and Symmetries in DNA Sequences

“…In this section we define some parameters, based on frequency distribution, which can measure the complexity of a DNA by computing the complexity of its representation in the complex plane (for a more detailed analysis see [46,47] and references therein). In particular, for the -length sequence, we define (see also [12,13,46,47]): 1) Randomness:…”

“…Almost all these papers are aiming to visualize the existence of regular patterns in nucleotide distributions [1,4,6,7,9,12,13,[16][17][18][19][20][21][22][23]25,[29][30][31][32][35][36][37]41,42,[45][46][47][48][49] and the existence of long range correlation [2,3,5,8,10,11,14,15,[24][25][26][27][28]33,34,[38][39][40][41]43,44]. At the moment, we can assume that nu...…”

“…Some interesting attempts to add more information concerning the nucleotide distribution and the existence of patterns were given by the wavelet analysis of DNA (see e.g. [1,3,4,12,13,17,[46][47][48][50][51][52][53]). In particular in [12,13,46,47,50,51] it has been shown that although the DNA sequence looks very similar to a random sequence the wavelet coefficients of the DNA walks are clearly distributed according to some rule while the random walks are not.…”