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{{short description|Ratio estimating the balance between nonsynonymous and synonymous substitutions}}
{{DISPLAYTITLE:Ka/Ks ratio}}
In [[genetics]], the '''Ka/Ks ratio''', also known as '''ω''' or '''''d''N/''d''S ratio''',{{efn|The terms Ka/Ks and ''d''N/''d''S are used interchangeably. Note however that ''D''n and ''D''s are different parameters from ''d''N and ''d''S (or ''K''A and ''K''S ). ''D''n and ''D''s are count estimates, which represent the total numbers of non-synonymous and synonymous substitutions.}} is used to estimate the balance between [[neutral mutation]]s, [[Negative selection (natural selection)|purifying selection]] and beneficial mutations acting on a set of [[Protein family|homologous protein-coding genes]]. It is calculated as the ratio of the number of [[nonsynonymous substitution]]s per non-synonymous site (Ka), in a given period of time, to the number of [[synonymous substitution]]s per synonymous site (Ks), in the same period. The latter are assumed to be neutral, so that the ratio indicates the net balance between deleterious and beneficial mutations. Values of Ka/Ks significantly above 1 are unlikely to occur without at least some of the [[mutation]]s being advantageous. If beneficial mutations are assumed to make little contribution, then Ka/Ks estimates the degree of [[biological constraints|evolutionary constraint]].

==Context==
Selection acts on variation in phenotypes, which are often the result of mutations in [[protein]]-coding [[genes]]. The [[genetic code]] is written in [[DNA sequences]] as [[codon]]s, groups of three [[nucleotide]]s. Each codon represents a single [[amino acid]] in a protein chain. However, there are more codons (64) than amino acids found in proteins (20), so many codons are effectively synonyms. For example, the DNA codons TTT and TTC both code for the amino acid [[Phenylalanine]], so a change from the third T to C makes no difference to the resulting protein. On the other hand, the codon GAG codes for [[Glutamic acid]] while the codon GTG codes for [[Valine]], so a change from the middle A to T does change the resulting protein, for better or (more likely) worse,{{efn|"Better" means that the change is advantageous and will be selected for by natural selection. "Worse" means that the change is harmful, and will be selected against.}} so the change is not a synonym. These changes are illustrated in the tables below.

The Ka/Ks ratio measures the relative rates of synonymous and nonsynonymous substitutions at a particular site.

{| class="wikitable"
|+ A [[point mutation]] causing a [[synonymous substitution]]
! Type of structure !! Before !! Change !! After || Result
|-
| [[Codon]] in a [[DNA sequence]] || TTT || harmless mutation;{{efn|Often but not always a "[[silent mutation]]".}} [[Synonymous substitution]]     || TTC ||
|-
| ↓ codes for || ↓ codes for ||   || ↓ codes for ||
|-
| [[Amino acid]] in a [[Protein]] || [[Phenylalanine]]   || no change || [[Phenylalanine]] || Normal protein, normal function
|}

{| class="wikitable"
|+ A [[point mutation]] causing a [[nonsynonymous substitution]]
! Type of structure !! Before !! Change !! After || Result
|-
| [[Codon]] in a [[DNA sequence]] || GAG || [[Missense mutation]]; [[Nonsynonymous substitution]] || GTG ||
|-
| ↓ codes for || ↓ codes for ||   || ↓ codes for ||
|-
| [[Amino acid]] in a [[Protein]] || [[Glutamic acid]]   || structural change || [[Valine]]             || Altered protein may or may not cause harm (e.g. disease) or give new advantage
|}

== Methods ==
Methods for estimating Ka and Ks use a [[sequence alignment]] of two or more nucleotide sequences of [[Homology (biology)|homologous]] genes that code for [[protein]]s (rather than being genetic switches, controlling development or the rate of activity of other genes). Methods can be classified into three groups: approximate methods, [[maximum-likelihood method]]s, and counting methods. However, unless the sequences to be compared are distantly related (in which case maximum-likelihood methods prevail), the class of method used makes a minimal impact on the results obtained; more important are the assumptions implicit in the chosen method.<ref name=Yang2000/>{{rp|498}}

=== Approximate methods ===
Approximate methods involve three basic steps: (1) counting the number of synonymous and nonsynonymous sites in the two sequences, or estimating this number by multiplying the sequence length by the proportion of each class of substitution;
(2) counting the number of synonymous and nonsynonymous substitutions; and (3) correcting for multiple substitutions.

These steps, particularly the latter, require simplistic assumptions to be made if they are to be achieved computationally; for reasons discussed later, it is impossible to exactly determine the number of multiple substitutions.<ref name=Yang2000/>

=== Maximum-likelihood methods ===
The maximum-likelihood approach uses [[probability theory]] to complete all three steps simultaneously.<ref name=Yang2000>{{cite journal | vauthors = Yang Z, Bielawski JP | title = Statistical methods for detecting molecular adaptation | journal = Trends in Ecology & Evolution | volume = 15 | issue = 12 | pages = 496–503 | date = December 2000 | pmid = 11114436 | pmc = 7134603 | doi = 10.1016/S0169-5347(00)01994-7 | citeseerx = 10.1.1.19.6537 }}</ref> It estimates critical parameters, including the divergence between sequences and the transition/transversion ratio, by deducing the most likely values to produce the input data.<ref name=Yang2000/>

=== Counting methods ===
In order to quantify the number of substitutions, one may reconstruct the ancestral sequence and record the inferred changes at sites (straight counting – likely to provide an underestimate); fitting the substitution rates at sites into predetermined categories ([[Bayesian inference|Bayesian]] approach; poor for small data sets); and generating an individual substitution rate for each [[codon]] (computationally expensive). Given enough data, all three of these approaches will tend to the same result.<ref name=Pond2005>{{cite journal | vauthors = Kosakovsky Pond SL, Frost SD | title = Not so different after all: a comparison of methods for detecting amino acid sites under selection | journal = Molecular Biology and Evolution | volume = 22 | issue = 5 | pages = 1208–1222 | date = May 2005 | pmid = 15703242 | doi = 10.1093/molbev/msi105 | doi-access = }}</ref>

== Interpreting results ==
The Ka/Ks ratio is used to infer the direction and magnitude of [[natural selection]] acting on protein coding genes. A ratio greater than 1 implies positive or Darwinian selection (driving change); less than 1 implies purifying or stabilizing selection (acting against change); and a ratio of exactly 1 indicates neutral (i.e. no) selection. However, a combination of positive and purifying selection at different points within the gene or at different times along its evolution may cancel each other out. The resulting averaged value can mask the presence of one of the selections and lower the seeming magnitude of another selection.

Of course, it is necessary to perform a statistical analysis to determine whether a result is significantly different from 1, or whether any apparent difference may occur as a result of a limited data set. The appropriate statistical test for an approximate method involves approximating dN − dS with a normal approximation, and determining whether 0 falls within the central region of the approximation. More sophisticated likelihood techniques can be used to analyse the results of a Maximum Likelihood analysis, by performing a [[chi-squared test]] to distinguish between a null model (Ka/Ks = 1) and the observed results.<ref name=Yang2000/>

== Utility ==
The Ka/Ks ratio is a more powerful test of the neutral model of evolution than many others available in [[population genetics]] as it requires fewer assumptions.<ref name=Yang2000/>

== Complications ==
There is often a [[systematic bias]] in the frequency at which various [[nucleotide]]s are swapped, as certain mutations are more probable than others.<ref name=Yang2000/> For instance, some lineages may swap C to T more frequently than they swap C to A. In the case of the amino acid [[Asparagine]], which is coded by the codons AAT or AAC, a high C->T exchange rate will increase the proportion of synonymous substitutions at this codon, whereas a high C→A exchange rate will increase the rate of non-synonymous substitutions. Because it is rather common for transitions (T↔C & A↔G) to be favoured over transversions (other changes),<ref name=Yang2000/> models must account for the possibility of non-homogeneous rates of exchange.<ref name=Hurst2002>{{cite journal | vauthors = Hurst LD | title = The Ka/Ks ratio: diagnosing the form of sequence evolution | journal = Trends in Genetics | volume = 18 | issue = 9 | pages = 486–487 | date = September 2002 | pmid = 12175810 | doi = 10.1016/S0168-9525(02)02722-1 }}</ref> Some simpler approximate methods, such as those of Miyata & Yasunaga and Nei & Gojobori, neglect to take these into account, which generates a faster computational time at the expense of accuracy; these methods will systematically overestimate N and underestimate S.<ref name=Yang2000/>

Further, there may be a bias in which certain codons are preferred in a gene, as a certain combination of codons may improve translational efficiency.<ref name=Yang2000/> A 2022 study reported that synonymous mutations in representative yeast genes are mostly strongly non-neutral, which calls into question the assumptions underlying use of the Ka/Ks ratio.<ref name=Shen2022>{{cite journal | vauthors = Shen X, Song S, Li C, Zhang J | title = Synonymous mutations in representative yeast genes are mostly strongly non-neutral | journal = Nature | volume = 606 | issue = 7915 | pages = 725–731 | date = June 2022 | pmid = 35676473 | doi = 10.1038/s41586-022-04823-w | pmc = 9650438 | bibcode = 2022Natur.606..725S | s2cid = 249520936 }}</ref>

In addition, as time progresses, it is possible for a site to undergo multiple modifications. For instance, a codon may switch from AAA→AAC→AAT→AAA. There is no way of detecting multiple substitutions at a single site, thus the estimate of the number of substitutions is always an underestimate. In addition, in the example above two non-synonymous and one synonymous substitution occurred at the third site; however, because substitutions restored the original sequence, there is no evidence of any substitution. As the divergence time between two sequences increases, so too does the amount of multiple substitutions. Thus "long branches" in a dN/dS analysis can lead to underestimates of both dN and dS, and the longer the branch, the harder it is to correct for the introduced noise.<ref name=Hurst2002/> Of course, the ancestral sequence is usually unknown, and two lineages being compared will have been evolving in parallel since their last common ancestor. This effect can be mitigated by constructing the ancestral sequence; the accuracy of this sequence is enhanced by having a large number of sequences descended from that common ancestor to constrain its sequence by [[phylogenetic]] methods.<ref name=Yang2000/>

Methods that account for biases in codon usage and transition/transversion rates are substantially more reliable than those that do not.<ref name=Yang2000/>

== Limitations ==
Although the Ka/Ks ratio is a good indicator of selective pressure at the sequence level, evolutionary change can often take place in the regulatory region of a gene which affects the level, timing or location of gene expression. Ka/Ks analysis will not detect such change. It will only calculate selective pressure within protein coding regions. In addition, selection that does not cause differences at an amino acid level—for instance, [[balancing selection]]—cannot be detected by these techniques.<ref name=Yang2000/>

Another issue is that heterogeneity within a gene can make a result hard to interpret. For example, if Ka/Ks = 1, it could be due to relaxed selection, or to a chimera of positive and purifying selection at the locus. A solution to this limitation would be to apply Ka/Ks analysis across many species at individual codons.

The Ka/Ks method requires a rather strong signal in order to detect selection.
In order to detect selection between lineages, then the selection, averaged over all sites in the sequence, must produce a Ka/Ks greater than one—quite a feat if regions of the gene are strongly conserved.
In order to detect selection at specific sites, then the Ka/Ks ratio must be greater than one when averaged over all included ''lineages'' at that site—implying that the site must be under selective pressure in all sampled lineages.
This limitation can be moderated by allowing the Ka/Ks rate to take multiple values across sites and across lineages; the inclusion of more lineages also increases the power of a sites-based approach.<ref name=Yang2000/>

Further, the method lacks the capability to distinguish between positive and negative nonsynonymous substitutions. Some [[amino acid]]s are chemically similar to one another, whereas other substitutions may place an amino acid with wildly different properties to its precursor. In most situations, a smaller chemical change is more likely to allow the protein to continue to function, and a large chemical change is likely to disrupt the chemical structure and cause the protein to malfunction. However, incorporating this into a model is not straightforward as the relationship between a nucleotide substitution and the effects of the modified chemical properties is very difficult to determine.<ref name=Yang2000/>

An additional concern is that the effects of time must be incorporated into an analysis, if the lineages being compared are closely related; this is because it can take a number of generations for natural selection to "weed out" deleterious mutations from a population, especially if their effect on fitness is weak.<ref>{{cite journal | vauthors = Rocha EP, Smith JM, Hurst LD, Holden MT, Cooper JE, Smith NH, Feil EJ | title = Comparisons of dN/dS are time dependent for closely related bacterial genomes | journal = Journal of Theoretical Biology | volume = 239 | issue = 2 | pages = 226–235 | date = March 2006 | pmid = 16239014 | doi = 10.1016/j.jtbi.2005.08.037 | bibcode = 2006JThBi.239..226R }}</ref><ref>{{cite journal | vauthors = Kryazhimskiy S, Plotkin JB | title = The population genetics of dN/dS | journal = PLOS Genetics | volume = 4 | issue = 12 | article-number = e1000304 | date = December 2008 | pmid = 19081788 | pmc = 2596312 | doi = 10.1371/journal.pgen.1000304 | doi-access = free }}</ref><ref>{{cite journal | vauthors = Peterson GI, Masel J | title = Quantitative prediction of molecular clock and ka/ks at short timescales | journal = Molecular Biology and Evolution | volume = 26 | issue = 11 | pages = 2595–2603 | date = November 2009 | pmid = 19661199 | pmc = 2912466 | doi = 10.1093/molbev/msp175 }}</ref><ref>{{cite journal | vauthors = Mugal CF, Wolf JB, Kaj I | title = Why time matters: codon evolution and the temporal dynamics of dN/dS | journal = Molecular Biology and Evolution | volume = 31 | issue = 1 | pages = 212–231 | date = January 2014 | pmid = 24129904 | pmc = 3879453 | doi = 10.1093/molbev/mst192 }}</ref> This limits the usefulness of the Ka/Ks ratio for comparing closely related populations.

== Individual codon approach ==
Additional information can be gleaned by determining the Ka/Ks ratio at specific codons within a gene sequence. For instance, the frequency-tuning region of an opsin may be under enhanced selective pressure when a species colonises and adapts to new environment, whereas the region responsible for initializing a nerve signal may be under purifying selection. In order to detect such effects, one would ideally calculate the Ka/Ks ratio at each site. However this is computationally expensive and in practise, a number of Ka/Ks classes are established, and each site is assigned to the best-fitting class.<ref name=Yang2000/>

The first step in identifying whether positive selection acts on sites is to compare a test where the Ka/Ks ratio is constrained to be < 1 in all sites to one where it may take any value, and see if permitting Ka/Ks to exceed 1 in some sites improves the fit of the model. If this is the case, then sites fitting into the class where Ka/Ks > 1 are candidates to be experiencing positive selection. This form of test can either identify sites that further laboratory research can examine to determine possible selective pressure; or, sites believed to have functional significance can be assigned into different Ka/Ks classes before the model is run.<ref name=Yang2000/>

==Notes==
{{notelist}}

== References==
{{reflist|30em}}

== Further reading ==
{{refbegin|30em}}
* {{cite journal | vauthors = Comeron JM | title = A method for estimating the numbers of synonymous and nonsynonymous substitutions per site | journal = Journal of Molecular Evolution | volume = 41 | issue = 6 | pages = 1152–1159 | date = December 1995 | pmid = 8587111 | doi = 10.1007/bf00173196 | s2cid = 19262479 | bibcode = 1995JMolE..41.1152C }}
* {{cite journal | vauthors = Goldman N, Yang Z | title = A codon-based model of nucleotide substitution for protein-coding DNA sequences | journal = Molecular Biology and Evolution | volume = 11 | issue = 5 | pages = 725–736 | date = September 1994 | pmid = 7968486 | doi = 10.1093/oxfordjournals.molbev.a040153 | doi-access = }}
* {{cite journal | vauthors = Hurst LD | title = The Ka/Ks ratio: diagnosing the form of sequence evolution | journal = Trends in Genetics | volume = 18 | issue = 9 | pages = 486–487 | date = September 2002 | pmid = 12175810 | doi = 10.1016/S0168-9525(02)02722-1 }}
* {{cite journal | vauthors = Ina Y | title = New methods for estimating the numbers of synonymous and nonsynonymous substitutions | journal = Journal of Molecular Evolution | volume = 40 | issue = 2 | pages = 190–226 | date = February 1995 | pmid = 7699723 | doi = 10.1007/bf00167113 | s2cid = 25430897 | bibcode = 1995JMolE..40..190I }}
* {{cite journal | vauthors = Li WH | title = Unbiased estimation of the rates of synonymous and nonsynonymous substitution | journal = Journal of Molecular Evolution | volume = 36 | issue = 1 | pages = 96–99 | date = January 1993 | pmid = 8433381 | doi = 10.1007/bf02407308 | s2cid = 21618703 | bibcode = 1993JMolE..36...96L }}
* {{cite journal | vauthors = Li WH, Wu CI, Luo CC | title = A new method for estimating synonymous and nonsynonymous rates of nucleotide substitution considering the relative likelihood of nucleotide and codon changes | journal = Molecular Biology and Evolution | volume = 2 | issue = 2 | pages = 150–174 | date = March 1985 | pmid = 3916709 | doi = 10.1093/oxfordjournals.molbev.a040343 | author-link = Wen-Hsiung Li | doi-access = free }}
* {{cite journal | vauthors = Muse SV, Gaut BS | title = A likelihood approach for comparing synonymous and nonsynonymous nucleotide substitution rates, with application to the chloroplast genome | journal = Molecular Biology and Evolution | volume = 11 | issue = 5 | pages = 715–724 | date = September 1994 | pmid = 7968485 | doi = 10.1093/oxfordjournals.molbev.a040152 | doi-access = free }}
* {{cite journal | vauthors = Nei M, Gojobori T | title = Simple methods for estimating the numbers of synonymous and nonsynonymous nucleotide substitutions | journal = Molecular Biology and Evolution | volume = 3 | issue = 5 | pages = 418–426 | date = September 1986 | pmid = 3444411 | doi = 10.1093/oxfordjournals.molbev.a040410 | doi-access = free }}
* {{cite journal | vauthors = Pamilo P, Bianchi NO | title = Evolution of the Zfx and Zfy genes: rates and interdependence between the genes | journal = Molecular Biology and Evolution | volume = 10 | issue = 2 | pages = 271–281 | date = March 1993 | pmid = 8487630 | doi = 10.1093/oxfordjournals.molbev.a040003 | doi-access = free }}
* {{cite journal | vauthors = Yang Z | title = PAML: a program package for phylogenetic analysis by maximum likelihood | journal = Computer Applications in the Biosciences | volume = 13 | issue = 5 | pages = 555–556 | date = October 1997 | pmid = 9367129 | doi = 10.1093/bioinformatics/13.5.555 | doi-access = free }}
* {{cite journal | vauthors = Yang Z, Nielsen R | title = Estimating synonymous and nonsynonymous substitution rates under realistic evolutionary models | journal = Molecular Biology and Evolution | volume = 17 | issue = 1 | pages = 32–43 | date = January 2000 | pmid = 10666704 | doi = 10.1093/oxfordjournals.molbev.a026236 | doi-access = }}
* {{cite journal | vauthors = Zhang Z, Li J, Yu J | title = Computing Ka and Ks with a consideration of unequal transitional substitutions | journal = BMC Evolutionary Biology | volume = 6 | issue = 1 | page = 44 | date = June 2006 | pmid = 16740169 | pmc = 1552089 | doi = 10.1186/1471-2148-6-44 | bibcode = 2006BMCEE...6...44Z | doi-access = free }}
* {{cite journal | vauthors = Zhang Z, Li J, Zhao XQ, Wang J, Wong GK, Yu J | title = KaKs_Calculator: calculating Ka and Ks through model selection and model averaging | journal = Genomics, Proteomics & Bioinformatics | volume = 4 | issue = 4 | pages = 259–263 | date = November 2006 | pmid = 17531802 | pmc = 5054075 | doi = 10.1016/S1672-0229(07)60007-2 }}
{{refend}}

== External links ==
* [https://code.google.com/p/kaks-calculator KaKs_Calculator]
* [https://services.cbu.uib.no/tools/kaks Free online server tool that calculates KaKs ratios among multiple sequences]
* [https://cran.r-project.org/web/packages/seqinr/index.html SeqinR: A free and open biological sequence analysis package for the R language that includes KaKs calculation]

{{MolecularEvolution}}

{{DEFAULTSORT:Ka Ks ratio}}
[[Category:Molecular evolution]]
[[Category:Genetics]]
[[Category:Statistical ratios]]

Ka/Ks ratio - История изменений

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