# Z curve

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.

## 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,...PN, with the coordinates xn, yn, and zn (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]

## References

1. ^ Zhang CT, Zhang R, Ou HY (2003). "The Z curve database: a graphic representation of genome sequences". Bioinformatics. 19 (5): 593–99. doi:10.1093/bioinformatics/btg041. PMID 12651717.
2. ^ Zhang, Ren; Zhang, Chun-Ting (February 1994). "Z Curves, An Intutive [sic] Tool for Visualizing and Analyzing the DNA Sequences". Journal of Biomolecular Structure and Dynamics. 11 (4): 767–782. doi:10.1080/07391102.1994.10508031. PMID 8204213.
3. ^ Yu, Chenglong; Deng, Mo; Zheng, Lu; He, Rong Lucy; Yang, Jie; Yau, Stephen S.-T. (2014-07-18). "DFA7, a New Method to Distinguish between Intron-Containing and Intronless Genes". PLOS ONE. 9 (7): e101363. Bibcode:2014PLoSO...9j1363Y. doi:10.1371/journal.pone.0101363. PMC 4103774. PMID 25036549.
4. ^ Zhang, Ren; Zhang, Chun-Ting (2014-04-01). "A Brief Review: The Z-curve Theory and its Application in Genome Analysis". Current Genomics. 15 (2): 78–94. doi:10.2174/1389202915999140328162433. ISSN 1389-2029. PMC 4009844. PMID 24822026.
5. ^ Zhang, C. T. (1997-08-07). "A symmetrical theory of DNA sequences and its applications". Journal of Theoretical Biology. 187 (3): 297–306. Bibcode:1997JThBi.187..297Z. doi:10.1006/jtbi.1997.0401. ISSN 0022-5193. PMID 9245572.
6. ^ Zhang R, Zhang CT (2005). "Identification of replication origins in archaeal genomes based on the Z-curve method". Archaea. 1 (5): 335–46. doi:10.1155/2005/509646. PMC 2685548. PMID 15876567.
7. ^ Worning P, Jensen LJ, Hallin PF, Staerfeldt HH, Ussery DW (February 2006). "Origin of replication in circular prokaryotic chromosomes". Environ. Microbiol. 8 (2): 353–61. Bibcode:2006EnvMi...8..353W. doi:10.1111/j.1462-2920.2005.00917.x. PMID 16423021. S2CID 3135023.
8. ^ Zhang, Ren; Zhang, Chun-Ting (2002-09-20). "Single replication origin of the archaeon Methanosarcina mazei revealed by the Z curve method". Biochemical and Biophysical Research Communications. 297 (2): 396–400. doi:10.1016/s0006-291x(02)02214-3. ISSN 0006-291X. PMID 12237132.
9. ^ Worning, Peder; Jensen, Lars J.; Hallin, Peter F.; Staerfeldt, Hans-Henrik; Ussery, David W. (2006-02-01). "Origin of replication in circular prokaryotic chromosomes". Environmental Microbiology. 8 (2): 353–361. Bibcode:2006EnvMi...8..353W. doi:10.1111/j.1462-2920.2005.00917.x. ISSN 1462-2912. PMID 16423021. S2CID 3135023.
10. ^ Guo FB, Ou HY, Zhang CT (2003). "ZCURVE: a new system for recognizing protein-coding genes in bacterial and archaeal genomes". Nucleic Acids Research. 31 (6): 1780–89. doi:10.1093/nar/gkg254. PMC 152858. PMID 12626720.
11. ^ Zhang CT, Zhang R (2004). "Isochore structures in the mouse genome". Genomics. 83 (3): 384–94. doi:10.1016/j.ygeno.2003.09.011. PMID 14962664.
12. ^ Zhang R, Zhang CT (2004). "A systematic method to identify genomic islands and its applications in analyzing the genomes of Corynebacterium glutamicum and Vibrio vulnificus CMCP6 chromosome I". Bioinformatics. 20 (5): 612–22. doi:10.1093/bioinformatics/btg453. PMID 15033867.
13. ^ Zhang R, Zhang CT (2003). "Identification of genomic islands in the genome of Bacillus cereus by comparative analysis with Bacillus anthracis". Physiological Genomics. 16 (1): 19–23. doi:10.1152/physiolgenomics.00170.2003. PMID 14600214.
14. ^ Zhang, C. T.; Lin, Z. S.; Yan, M.; Zhang, R. (1998-06-21). "A novel approach to distinguish between intron-containing and intronless genes based on the format of Z curves". Journal of Theoretical Biology. 192 (4): 467–473. Bibcode:1998JThBi.192..467Z. doi:10.1006/jtbi.1998.0671. ISSN 0022-5193. PMID 9680720.
15. ^ Zhang, Ren; Zhang, Chun-Ting (2002-09-20). "Single replication origin of the archaeon Methanosarcina mazei revealed by the Z curve method". Biochemical and Biophysical Research Communications. 297 (2): 396–400. doi:10.1016/s0006-291x(02)02214-3. ISSN 0006-291X. PMID 12237132.
16. ^ Zheng, Wen-Xin; Chen, Ling-Ling; Ou, Hong-Yu; Gao, Feng; Zhang, Chun-Ting (2005-08-01). "Coronavirus phylogeny based on a geometric approach". Molecular Phylogenetics and Evolution. 36 (2): 224–232. Bibcode:2005MolPE..36..224Z. doi:10.1016/j.ympev.2005.03.030. ISSN 1055-7903. PMC 7111192. PMID 15890535.