Ka/Ks ratio

Ratio estimating the balance between nonsynonymous and synonymous substitutions
DISPLAYTITLE:Ka/Ks ratio
In genetics, the Ka/Ks ratio, also known as ω or dN/dS ratio, is used to estimate the balance between neutral mutations, purifying selection and beneficial mutations acting on a set of homologous protein coding genes. It is calculated as the ratio of the number of nonsynonymous substitutions per non synonymous site (Ka), in a given period of time, to the number of synonymous substitutions 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 mutations being advantageous. If beneficial mutations are assumed to make little contribution, then Ka/Ks estimates the degree of evolutionary constraint.

Methods for estimating Ka and Ks use a sequence alignment of two or more nucleotide sequences of homologous genes that code for proteins (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 methods, 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. 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.

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. 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.

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. This limits the usefulness of the Ka/Ks ratio for comparing closely related populations.

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. 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.