Codon Evolution Mechanisms and Models

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194 MEASURING CODON USAGE BIAS indices: INCA by Supek and Vlahovicek (2004) and GCUA by McInerney (1998). Implementations also exist in libraries of common programming languages, such as, BioPerl by Brenner et al. (2002), seqinR by Charif et al. (2005), and EMBOSS by Rice et al. (2000). Easy access under one framework to the bulk of codon usage bias indices would facilitate comparison, benchmark studies and performance analysis. 13.5.1 Relative codon frequencies Many indices often require the codon counts to be normalized into codon frequencies to remove the dependence on gene length. Frequencies can be computed in a number of ways. The simplest way is to normalize by the sum of all codons in the vector: � gc = oc oc c∈C , (13.1) where g denotes a global frequency. This can also be expressed in the double-index notation: gac = � oac � a∈A c∈Ca . (13.2) oac This normalization has the problem that it will overweight frequent amino acids. It is therefore usually better to normalize within each amino acid separately to avoid the confounding influence of amino acid content: fac = � oac c∈Ca oac (13.3) where f denotes the frequency within amino acid a. The relative synonymous codon usage (RSCU) compensates for both the different number of synonymous codons for the various amino acids, as well as for the differing amino acid frequencies: rac = 1 ka oac � c∈Ca oac = oac , (13.4) oa where ka is the number of synonymous codons and r denotes a relative synonymous frequency (Sharp et al., 1986). The RSCU values express the relationship between the observed number of codons and the number of times the codon would be observed if the synonymous codon usage was completely random (no codon usage bias). For average synonymous codon usage (no codon bias) the RSCU is 1. For codon usage more infrequent than the average codon usage, the RSCU is less than one, and for more frequent usage than the average for the amino acid, the RSCU is greater than 1. Another way of normalizing the data is to use the relative adaptiveness, w, in which the frequency of each synonymous codons is normalized by the frequency of the most frequent codon. Thus the most frequent codon will have a relative adaptiveness of 1, while the others will have a relative adaptiveness of less than one. The relative adaptiveness is: wac = oac max oac c∈Ca . (13.5) Amino acids decoded by one codon (Trp and Met for the standard genetic code) also have a relative adaptiveness of 1 and are often neglected, as they do not contribute additional information. Stop codons are also often disregarded, since their occurrence is rare compared to other codons and usually strongly biased toward one codon. 13.5.2 Measures based on reference Many indices compare the query gene to a reference set of genes with some desirable quality. The idea is that certain profiles of codon usage are optimal. Assignment of optimal codons requires strong assumptions, since the factors shaping the codon usage may differ among genes and genomes. The reference set can be defined from either first principles (e.g. Fop) or using a reference set of highly expressed genes (e.g. CAI). Highly expressed genes are under stronger translational selection and the synonymous codons are under stronger selective constraints. 13.5.2.1 Frequency of optimal codons (Fop) The frequency of optimal codons (Fop), the ratio of the number of optimal codons used to the total number of synonymous codons, was one of the first codon usage measures proposed (Ikemura, 1981b). The optimal codons can be defined according to nucleotide chemistry, codon usage bias, or
tRNA availability. In short: (1) pyrimidine twocodon amino acids prefer A-ending codons over G-ending; (2) purine two-codon amino acids prefer C-ending codons over U-ending; (3) if there exists a tRNA with inosine, the wobble position prefer Uand C-ending codons over those with A-endings; (4) codons with higher tRNA abundance are preferred; and (5) codons that are decoded by more than one different tRNA isoacceptors. The constraint of tRNA abundance is probably the most important constraint (Ikemura, 1985). Therefore, a convenient way to define translationally optimal codons is those codons that are cognate to the most abundant tRNA isoacceptor in each codon family. The tRNA abundances can be inferred from the tRNA gene copy number of genome data. Since tRNA abundance and codon usage are highly correlated, optimal codons can be alternatively defined as those that are the most common. The frequency of optimal codons is the ratio of the number of optimal codons to the total number of codons: Fop = oopt . (13.6) otot The number of optimal codons is: oopt = � oc. (13.7) c∈Copt The subset of optimal codons, Copt, is defined according to the above criteria, from all the codons C that are included in the analysis. Amino acids with one codon do not contribute any information and are omitted. Amino acids with one isoacceptor are often excluded when the optimal codon can not be determined. The total number of codons in a sequence otot is the total number of codons included in the analysis. 13.5.2.2 Codon bias index (CBI) The codon bias index also measures the extent to which preferred codons are used in a gene (Bennetzen and Hall, 1982). The preferred codons are defined as codons frequent in highly expressed genes and codons cognate to the major tRNA species. It is similar to Fop, but uses the expected usage as a scaling factor and thus is normalized between −1 and 1. A value of 1 means only preferred codons are used, zero means random choice MEASURES OF CODON BIAS 195 and less than zero implies greater use of nonpreferred codons: CBI = oopt − erand , (13.8) otot − erand where oopt is the number of preferred optimal codons, otot is the total number of codons, and erand is the expected number of optimal codons if random codon assignments were made for each amino acid. erand is used to account for the random effect of codon usage and is computed as follows: erand = � a∈A oa n opt a ka , (13.9) where oa is the number of occurrences of amino acid a in the sequence, n opt a is the number of instances of optimal codons for amino acid a, andkathe codon redundancy. Amino acids with only one codon are excluded from the analysis, as are occasionally amino acids that show little preference towards a single codon (e.g. Asp in Yeast). 13.5.2.3 Codon usage bias (B) The codon usage bias (B) assesses the codon bias of a test set of genes (or group of genes) relative to a second reference set of genes (Karlin and Mrázek, 1996; Karlin et al., 1998). The reference set, composed of a gene class, an entire genome, or a single gene, is used as a standard to which other genes or groups of genes can be compared. This metric is defined as the amino acid frequency weighted sum of distances of the relative codon usage frequencies between the two sets, f and f ref : B= � Fad(fa, f ref a ), (13.10) a∈A where Fa is the frequency of the amino acid a in the test set, vectors fa and fref a are the codon frequency vectors for amino acid a in the test and reference set respectively, and d is the 1-norm distance between the codon vectors of amino acid a: d(fa, f ref a )=� c∈Ca | fac, f ref ac | (13.11)
Page 1 and 2: Codon Evolution Mechanisms and Mode
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Page 13 and 14: � 1 tAI = exp otot � c∈C oc l
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Page 25 and 26: log mRNA log Protein log k s 3 2 1
Page 27 and 28: scope of this review, since for man
Page 29 and 30: Fuglsang, A. (2004). Bioinformatic
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