Z curve

This article is about a method for genome analysis. For the space filling curve, see Z-order (curve). For the weighting curve, see Z-weighting.

The Z curve (or Z-curve) method is a bioinformatics algorithm for genome analysis. The Z-curve is a three-dimensional curve that constitutes a unique representation of a DNA sequence, i.e., for the Z-curve and the given DNA sequence each can be uniquely reconstructed from the other.^[1] The resulting curve has a zigzag shape, hence the name Z-curve.

Z curve of C.elegans chromosome III

Background

The Z Curve method was first created in 1994 as a way to visually map a DNA or RNA sequence. Different properties of the Z curve, such as its symmetry and periodicity can give unique information on the DNA sequence.^[2] The Z curve is generated from a series of nodes, P₀, P₁,...P_N, with the coordinates x_n, y_n, and z_n (n=0,1,2...N, with N being the length of the DNA sequence). The Z curve is created by connecting each of the nodes sequentially.^[3]

${\displaystyle x_{n}=(A_{n}+G_{n})-(C_{n}+T_{n})}$

${\displaystyle y_{n}=(A_{n}+C_{n})-(G_{n}+T_{n})}$

${\displaystyle z_{n}=(A_{n}+T_{n})-(C_{n}+G_{n})}$

${\displaystyle n=0,1,2,...N}$

Applications

Information on the distribution of nucleotides in a DNA sequence can be determined from the Z curve. The four nucleotides are combined into six different categories. The nucleotides are placed into each category by some defining characteristic and each category is designated a letter.^[4]

Purine	R = A, G	Amino	M = A, C	Weak Hydrogen Bonds	W = A, T
Pyrimidine	Y = C, T	Keto	K = G, T	Strong Hydrogen Bonds	S = G, C

The x, y, and z components of the Z curve display the distribution of each of these categories of bases for the DNA sequence being studied. The x-component represents the distribution of purines and pyrimidine bases (R/Y). The y-component shows the distribution of amino and keto bases (M/K) and the z-component shows the distribution of strong-H bond and weak-H bond bases (S/W) in the DNA sequence.^[5]

The Z-curve method has been used in many different areas of genome research, such as replication origin identification,^[6][7][8][9], ab initio gene prediction,^[10] isochore identification,^[11] genomic island identification^[12] and comparative genomics.^[13] Analysis of the Z curve has also been shown to be able to predict if a gene contains introns,^[14]

Research

Experiments have shown that the Z curve can be used to identify the replication origin in various organisms. One study analyzed the Z curve for multiple species of Archaea and found that the oriC is located at a sharp peak on the curve followed by a broad base. This region was rich in AT bases and had multiple repeats, which is expected for replication origin sites.^[15] This and other similar studies were used to generate a program that could predict the origins of replication using the Z curve.

The Z curve has also been experimentally used to determine phylogenetic relationships. In one study, a novel coronavirus in China was analyzed using sequence analysis and the Z curve method to determine its phylogenetic relationship to other coronaviruses. It was determined that similarities and differences in related species can quickly by determined by visually examining their Z curves. An algorithm was created to identify the geometric center and other trends in the Z curve of 24 species of coronaviruses. The data was used to create a phylogenetic tree. The results matched the tree that was generated using sequence analysis. The Z curve method proved superior because while sequence analysis creates a phylogenetic tree based solely on coding sequences in the genome, the Z curve method analyzed the entire genome.^[16]