A Brief Review: The Z-curve Theory and its Application in Genome Analysis

Abstract

In theoretical physics, there exist two basic mathematical approaches, algebraic and geometrical methods, which, in most cases, are complementary. In the area of genome sequence analysis, however, algebraic approaches have been widely used, while geometrical approaches have been less explored for a long time. The Z-curve theory is a geometrical approach to genome analysis. The Z-curve is a three-dimensional curve that represents a given DNA sequence in the sense that each can be uniquely reconstructed given the other. The Z-curve, therefore, contains all the information that the corresponding DNA sequence carries. The analysis of a DNA sequence can then be performed through studying the corresponding Z-curve. The Z-curve method has found applications in a wide range of areas in the past two decades, including the identifications of protein-coding genes, replication origins, horizontally-transferred genomic islands, promoters, translational start sides and isochores, as well as studies on phylogenetics, genome visualization and comparative genomics. Here, we review the progress of Z-curve studies from aspects of both theory and applications in genome analysis.

Assessing the Effects of Data Selection and Representation on the Development of Reliable E. coli Sigma 70 Promoter Region Predictors

“…VWZ method extracts Z-curve descriptors [ 67 ] of k-mer features (for k = 1, …, 6) and uses a partial least squares (PLS) classifier combined with an iterative feature selection procedure to eliminate irrelevant and highly-correlated features. The method was evaluated on two data sets: Dataset-1 contains 576 σ 70 promoters (positive samples) and 836 coding fragments (negative samples) of E. coli; Dataset-2 contains the same 576 σ 70 promoters (positive samples) and 825 non-coding fragments (negative samples) of E. coli.…”

Numerical Characterization of Protein Sequences Based on the Generalized Chou’s Pseudo Amino Acid Composition

“…Early attempts towards graphical representations of DNA were made by Hamori and Ruskin in 1983 [3], Hamori in 1985 [4], and Gates in 1985 [5]. Afterwards, more graphical representations of DNA sequences were well developed by researchers [1,2,[6][7][8][9][10][11][12][13][14][15]. In comparison with DNA, graphical representations of proteins emerged only very recently [2,[16][17][18][19][20][21][22][23][24][25][26][27].…”

Novel Graphical Representation and Numerical Characterization of DNA Sequences

“…In 2000, Randic et al [8] generalized these 2-D graphical representations to a 3-D graphical representation, in which the center of a cube is chosen as the origin of the Cartesian (x,y,z) coordinate system, and the four corners with coordinates (+1,´1,´1), (´1,+1,´1), (´1,´1,+1), and (+1,+1,+1) are assigned to the four bases. Some other graphical representations of bio-sequences and their applications in the field of biological science and technology can be found in [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”