Towards a resolution on the inherent methodological weakness of the "effective number of codons used by a gene"

Recently Anders Fuglsang provided a modified way for calculating N(c) when biased discrepancy is present in a gene [Biochem. Biophys. Res. Commun. 317 (2004) 957]. Instead of taking the average codon homozygosity for each synonymous family type (as proposed by Wright) [Gene 87 (1990) 23] Fuglsang considered codon homozygosity of each amino acid individually. Marsashi and Najafabadi [Biochem. Biophys. Res. Commun. 324 (2004) 1] in their recent article demonstrated that the readjustment for overestimation at the level of individual amino acids results in loss of considerable amount of information. Immediately after the publication of Marsashi and Najafabadi, Fuglsang proposed that codon homozygosities can be calculated based on the classical population genetics [Biochem. Biophys. Res. Commun. 327 (2005) 1]. Though Fuglsang's approach is a novel one, it fails when any of the amino acids are absent in a gene. However, the inherent cause of overestimation at the level of individual amino acids is still obscured in the literature. Here in this communication we have presented a general condition where effective number of codons is overestimated using Wright's formula and also we propose a new way to calculate N(c), which is independent of amino acid composition.     

Estimating the unbiased estimator theta for population genetic survey data

We consider a method of approximating Weir and Cockerham's theta, an unbiased estimator of genetic population structure, using values readily available from published studies using biased estimators (Wright's F(ST) or Nei's G(ST)). The estimation algorithm is shown to be useful for both model populations and real-world avian populations. However, the correlation between Wright's F(ST) and Weir and Cockerham's theta is strong when compared among 39 empirical avian datasets. Thus, the advantage of approximating an unbiased estimator is unclear considering the small actual effect of theta's bias-removing power on empirical datasets.     

A study of the purine/pyrimidine codon occurrence with a reduced centered variable and an evaluation compared to the frequency statistic

With the three-letter alphabet [R,Y,N] (R = purine, Y = pyrimidine, N = R or Y), there are 26 codons (NNN being excluded): RNN,...,NNY (six codons at two unspecified bases N), RRN,...,NYY (12 codons at one unspecified base N), RRR,...,YYY (eight specified codons). A statistical methodology that uses the codon frequency and a reduced centered variable leads to similar results for a codon occurrence study, regardless of gene function and regardless of a particular protein coding gene taxonomic population. Therefore, this variable can be considered a new codon usage index, whose use removes certain nonsignificant results found with the frequency statistic. This methodology identifies the common and rare codons (i.e., the codons having the highest and lowest occurrence) and leads to a model of codon evolution at three successive states: RNN, then RNY, and finally RYY. Some biological relations between this model and the YRY(N)6YRY preferential occurrence are also presented.     

Construction of "small-intelligent" focused mutagenesis libraries using well-designed combinatorial degenerate primers

Site-saturation mutagenesis is a powerful tool for protein optimization due to its efficiency and simplicity. A degenerate codon NNN or NNS (K) is often used to encode the 20 standard amino acids, but this will produce redundant codons and cause uneven distribution of amino acids in the constructed library. Here we present a novel "small-intelligent" strategy to construct mutagenesis libraries that have a minimal gene library size without inherent amino acid biases, stop codons, or rare codons of Escherichia coli by coupling well-designed combinatorial degenerate primers with suitable PCR-based mutagenesis methods. The designed primer mixture contains exactly one codon per amino acid and thus allows the construction of small-intelligent mutagenesis libraries with one gene per protein. In addition, the software tool DC-Analyzer was developed to assist in primer design according to the user-defined randomization scheme for library construction. This small-intelligent strategy was successfully applied to the randomization of halohydrin dehalogenases with one or two randomized sites. With the help of DC-Analyzer, the strategy was proven to be as simple as NNS randomization and could serve as a general tool to efficiently randomize target genes at positions of interest.     

Evolution of the mitochondrial genetic code II. Reassignment of codon AUA from isoleucine to methionine

Summary The reassignment of codon AUA from isoleucine to methionine during mitochondrial evolution may be explained by the codon reassignment (capture) hypothesis without assuming direct replacement of isoleucine by methionine in mitochondrial proteins. According to this hypothesis, codon AUA would have disappeared from the reading frames of messenger RNA. AUA codons would have mutated mainly to AUU isoleucine codons because of constraints resulting from elimination of tRNA Ile with anticodon *CAU (in which *C is lysidine). Later, tRNA Met (CAU) would have undergone structural changes enabling it to pair with both AUG and AUA. AUA codons, formed by mutations of other codons, including AUG, would have reappeared and would have been translated as methionine.     

Preferential carcinogen-DNA adduct formation at codons 12 and 14 in the human K-ras gene and their possible mechanisms

In the ras gene superfamily, codon 12 (-TGGTG-) of the K-ras gene is the most frequently mutated codon in human cancers. Recently, we have found that bulky chemical carcinogens preferentially form DNA adducts at codons 12 and 14 (-CGTAG-) in the K-ras gene in normal human bronchial epithelial (NHBE) cells. Furthermore, DNA adducts formed at codon 12 of the K-ras gene are poorly repaired compared with those at other codons including codon 14. These results suggest that targeted carcinogen-DNA adduct formation is a major reason for the observed high mutation frequency at codon 12 of the K-ras gene in human cancers. This preferential carcinogen-DNA adduct formation at codons 12 and 14 could result from effects of (1) primary sequences of these codons and their surrounding codons in the K-ras gene, (2) the chromatin structure, and/or (3) epigenetic factors such as C5 cytosine methylation or other DNA modifications at these codons and their surrounding codons. To distinguish these possibilities, we have introduced modifications with benzo[a]pyrene diol epoxide, N-hydroxy-2-aminofluorene, and aflatoxin B1 8,9-epoxide in (1) naked intact genomic DNA isolated from NHBE cells, (2) fragmented genomic DNA digested by restriction enzymes, and (3) in vitro synthesized DNA fragments containing the K-ras gene exon 1 sequence with or without methylation of the cytosines at CpG sites and the cytosines pairing with the guanines of codons 12 and 14. The distribution of carcinogen-DNA adducts in the K-ras gene was mapped at the nucleotide sequence level using the UvrABC nuclease incision method with or without the ligation-mediated polymerase chain reaction technique. We have found that carcinogens preferentially form adducts at codons 12 and 14 in the K-ras gene exon 1 in intact as well as in fragmented genomic DNA. In contrast, this preferential DNA adduct formation at codons 12 and 14 was not observed in PCR-amplified DNA fragments containing the K-ras gene exon 1 sequence. Methylation of the cytosine at the CpG site of codon 14, or the cytosine pairing with guanine of codon 14, greatly enhanced carcinogen-DNA adduct formation at codon 14 but did not affect carcinogen-DNA adduct formation at codon 12. Methylation of the cytosine pairing with the guanine of codon 12 also did not enhance carcinogen-DNA adduct formation at codon 12. Furthermore, we found that the cytosine at the CpG site of codon 14 is highly methylated in NHBE cells. These results suggest that cytosine methylation at the CpG site is the major reason for the preferential DNA damage at codon 14 and that epigenetic modification(s) other than cytosine methylation may contribute to the preferential DNA damage at codon 12 of the K-ras gene.     

Genome-wide selection on codon usage at the population level in the fungal model organism Neurospora crassa

Many organisms exhibit biased codon usage in their genome, including the fungal model organism Neurospora crassa. The preferential use of subset of synonymous codons (optimal codons) at the macroevolutionary level is believed to result from a history of selection to promote translational efficiency. At present, few data are available about selection on optimal codons at the microevolutionary scale, that is, at the population level. Herein, we conducted a large-scale assessment of codon mutations at biallelic sites, spanning more than 5,100 genes, in 2 distinct populations of N. crassa: the Caribbean and Louisiana populations. Based on analysis of the frequency spectra of synonymous codon mutations at biallelic sites, we found that derived (nonancestral) optimal codon mutations segregate at a higher frequency than derived nonoptimal codon mutations in each population; this is consistent with natural selection favoring optimal codons. We also report that optimal codon variants were less frequent in longer genes and that the fixation of optimal codons was reduced in rapidly evolving long genes/proteins, trends suggestive of genetic hitchhiking (Hill-Robertson) altering codon usage variation. Notably, nonsynonymous codon mutations segregated at a lower frequency than synonymous nonoptimal codon mutations (which impair translational efficiency) in each N. crassa population, suggesting that changes in protein composition are more detrimental to fitness than mutations altering translation. Overall, the present data demonstrate that selection, and partly genetic interference, shapes codon variation across the genome in N. crassa populations.     

An evaluation of inbreeding measures using a whole-genome sequenced cattle pedigree

The estimation of the inbreeding coefficient (F) is essential for the study of inbreeding depression (ID) or for the management of populations under conservation. Several methods have been proposed to estimate the realized F using genetic markers, but it remains unclear which one should be used. Here we used whole-genome sequence data for 245 individuals from a Holstein cattle pedigree to empirically evaluate which estimators best capture homozygosity at variants causing ID, such as rare deleterious alleles or loci presenting heterozygote advantage and segregating at intermediate frequency. Estimators relying on the correlation between uniting gametes (F_UNI) or on the genomic relationships (F_GRM) presented the highest correlations with these variants. However, homozygosity at rare alleles remained poorly captured. A second group of estimators relying on excess homozygosity (F_HOM), homozygous-by-descent segments (F_HBD), runs-of-homozygosity (F_ROH) or on the known genealogy (F_PED) was better at capturing whole-genome homozygosity, reflecting the consequences of inbreeding on all variants, and for young alleles with low to moderate frequencies (0.10 < . < 0.25). The results indicate that F_UNI and F_GRM might present a stronger association with ID. However, the situation might be different when recessive deleterious alleles reach higher frequencies, such as in populations with a small effective population size. For locus-specific inbreeding measures or at low marker density, the ranking of the methods can also change as F_HBD makes better use of the information from neighboring markers. Finally, we confirmed that genomic measures are in general superior to pedigree-based estimates. In particular, F_PED was uncorrelated with locus-specific homozygosity.Subject terms: Conservation genomics, Animal breeding, Inbreeding     

A型流感病毒NS1基因密码子去优化改造引起病毒毒力减弱

根据A型流感病毒密码子使用偏嗜性,选取稀有密码子对A/Puerto Rico/8/34(H1N1)病毒NS1基因内部110个氨基酸区域进行密码子同义突变改造,并全基因合成NS基因,利用反向遗传操作技术拯救出含有密码子去优化NS1基因的重组病毒(deoNS)。体外细胞噬斑形成实验和病毒生长曲线证明该病毒在MDCK细胞内的感染和复制能力比野生型病毒低约1000倍;BALB/c小鼠体内致病力实验证明deoNS病毒不能引起小鼠发病和死亡,该病毒在小鼠肺内的复制滴度比野生型病毒低100～1000倍。本研究探索了通过基因组密码子去优化改造途径降低A型流感病毒毒力的可行性,首次证明流感病毒NS1基因密码子去优化同义突变可以降低病毒毒力,为流感减毒活疫苗的研究提供了新的思路。     

Unbiased relatedness estimation in structured populations

Knowledge of the genetic relatedness between individuals is important in many research areas in quantitative genetics, conservation genetics, forensics, evolution, and ecology. In the absence of pedigree records, relatedness can be estimated from genetic marker data using a number of estimators. These estimators, however, make the critical assumption of a large random mating population without genetic structures. The assumption is frequently violated in the real world where geographic/social structures or nonrandom mating usually lead to genetic structures. In this study, I investigated two approaches to the estimation of relatedness between a pair of individuals from a subpopulation due to recent common ancestors (i.e., relatedness is defined and measured with the current focal subpopulation as reference). The indirect approach uses the allele frequencies of the entire population with and without accounting for the population structure, and the direct approach uses the allele frequencies of the current focal subpopulation. I found by simulations that currently widely applied relatedness estimators are upwardly biased under the indirect approach, but can be modified to become unbiased and more accurate by using Wright's F(st) to account for population structures. However, the modified unbiased estimators under the indirect approach are clearly inferior to the unmodified original estimators under the direct approach, even when small samples are used in estimating both allele frequencies and relatedness.     

Correcting the Bias of Empirical Frequency Parameter Estimators in Codon Models

Markov models of codon substitution are powerful inferential tools for studying biological processes such as natural selection and preferences in amino acid substitution. The equilibrium character distributions of these models are almost always estimated using nucleotide frequencies observed in a sequence alignment, primarily as a matter of historical convention. In this note, we demonstrate that a popular class of such estimators are biased, and that this bias has an adverse effect on goodness of fit and estimates of substitution rates. We propose a “corrected” empirical estimator that begins with observed nucleotide counts, but accounts for the nucleotide composition of stop codons. We show via simulation that the corrected estimates outperform the de facto standard estimates not just by providing better estimates of the frequencies themselves, but also by leading to improved estimation of other parameters in the evolutionary models. On a curated collection of sequence alignments, our estimators show a significant improvement in goodness of fit compared to the approach. Maximum likelihood estimation of the frequency parameters appears to be warranted in many cases, albeit at a greater computational cost. Our results demonstrate that there is little justification, either statistical or computational, for continued use of the -style estimators.     

The 'effective number of codons' revisited

Frank Wright [Gene 87 (1990) 23] derived a formula for calculation of a quantity termed the 'effective number of codons' (Nc) based on codon homozygosities. This quantity is a number between 20 and 61 and tells to what degree the codon usage in a gene is biased, i.e., it approaches 20 codons for the extremely biased genes, and approaches 61 for the genes where all possible codons are used with no preference. Among the different measures of codon bias Nc is considered the most useful and has found widespread use in papers dealing with codon usage phenomena. In this paper, the mathematical behaviours of codon homozygosities and Nc are evaluated, using Escherichia coli as the model organism. The results indicate that the classical formula for calculation of Nc could appropriately be substituted under circumstances, where there is bias discrepancy, i.e., when one amino acid (or more) within a degeneracy group is associated with strong codon bias while at the same time others in the same degeneracy group have little bias. An alternative estimator, termed Nc, is proposed and tested against Nc, and performs better when there is such bias discrepancy.     

Genome-wide analysis of codon usage bias patterns in an enterotoxigenic <Emphasis Type="Italic">Escherichia coli</Emphasis> F18 strain

Enterogenic Escherichia coli (ETEC) F18 strains are the main pathogenic bacteria causing severe diarrhea in humans and domestic animals. However, the information about synonymous codon usage pattern of ETEC F18 genome remains unclear. We conducted a genome-wide analysis of synonymous codon usage patterns in the ETEC F18 strain SRA: SAMN02471895. After filtering of the complete genome sequence, 4327 coding sequences were analyzed using multivariate statistical methods to calculate synonymous codon usage patterns and to evaluate the influence of various factors in shaping the codon usage. The mean GC content was 51.38%, with a slight preference for G/C-ending codons. Twenty-two codons were determined as ‘‘optimal codons”. ENC plots showed some of the genes were on or close to the expected curve, while only points with low-ENC values were below the curve. PR2 analysis showed that GC and AT were not used proportionally, suggesting major roles for mutational pressure and natural selection in shaping usage. Neutrality plots showed a significant correlation between GC12 and GC3, suggesting that mutational pressure is responsible for nucleotide composition in shaping the strength of codon usage. Translational selection was the main factor shaping the codon usage pattern of ETEC F18 genome, while other factors such as protein length, GRAVY and ARO values also influenced codon usage to some extent. We analyzed the codon usage pattern systematically and identified the factors shaping codon usage bias in the ETEC F18 genome. Such information further elucidates the mechanisms of synonymous codon usage bias and provides the basis of molecular genetic engineering and evolutionary studies.     

Synonymous codon selection controls in vivo turnover and amount of mRNA in Escherichia coli bla and ompA genes.

A number of silent codon changes were made in two Escherichia coli genes. For the ompA gene, the replacement of seven consecutive frequently used codons with synonymous infrequently used codons reduced the ompA mRNA level and its half-life. For the bla gene, the exchange of 24 codons for the most frequently used synonymous codons extended the bla mRNA half-life. A modification of ribosome traffic could account for these observations.     

Introns are cis effectors of the nonsense-codon-mediated reduction in nuclear mRNA abundance.

The translation of human triosephosphate isomerase (TPI) mRNA normally terminates at codon 249 within exon 7, the final exon. Frameshift and nonsense mutations of the type that cause translation to terminate prematurely at or upstream of codon 189 within exon 6 reduce the level of nuclear TPI mRNA to 20 to 30% of normal by a mechanism that is not a function of the distance of the nonsense codon from either the translation initiation or termination codon. In contrast, frameshift and nonsense mutations of another type that cause translation to terminate prematurely at or downstream of codon 208, also within exon 6, have no effect on the level of nuclear TPI mRNA. In this work, quantitations of RNA that derived from TPI alleles in which nonsense codons had been generated between codons 189 and 208 revealed that the boundary between the two types of nonsense codons resides between codons 192 and 195. The analysis of TPI gene insertions and deletions indicated that the positional feature differentiating the two types of nonsense codons is the distance of the nonsense codon upstream of intron 6. For example, the movement of intron 6 to a position downstream of its normal location resulted in a concomitant downstream movement of the boundary between the two types of nonsense codons. The analysis of intron 6 mutations indicated that the intron 6 effect is stipulated by the 88 nucleotides residing between the 5' and 3' splice sites. Since the deletion of intron 6 resulted in only partial abrogation of the nonsense codon-mediated reduction in the level of TPI mRNA, other sequences within TPI pre-mRNA must function in the effect. One of these sequences may be intron 2, since the deletion of intron 2 also resulted in partial abrogation of the effect. In experiments that switched introns 2 and 6, the replacement of intron 6 with intron 2 was of no consequence to the effect of a nonsense codon within either exon 1 or exon 6. In contrast, the replacement of intron 2 with intron 6 was inconsequential to the effect of a nonsense codon in exon 6 but resulted in partial abrogation of a nonsense codon in exon 1.     

Rabies virus (RV) glycoprotein expression levels are not critical for pathogenicity of RV

Previous comparisons of different rabies virus (RV) strains suggested an inverse relationship between pathogenicity and the amount of glycoprotein produced in infected cells. In order to provide more insight into this relationship, we pursued an experimental approach that allowed us to alter the glycoprotein expression level without altering the glycoprotein sequence, thereby eliminating the contribution of amino acid changes to differences in viral virulence. To this end, we constructed an infectious clone of the highly pathogenic rabies virus strain CVS-N2c and replaced its cognate glycoprotein gene with synthetic versions in which silent mutations were introduced to replace wild-type codons with the most or least frequently used synonymous codons. A recombinant N2c variant containing the fully codon-optimized G gene and three variants carrying a partially codon-deoptimized G gene were recovered on mouse neuroblastoma cells and shown to express 2- to 3-fold more and less glycoprotein, respectively, than wild-type N2c. Pathogenicity studies in mice revealed the WT-N2c virus to be the most pathogenic strain. Variants containing partially codon-deoptimized glycoprotein genes or the codon-optimized gene were less pathogenic than WT-N2c but still caused significant mortality. We conclude that the expression level of the glycoprotein gene does have an impact on pathogenicity but is not a dominant factor that determines pathogenicity. Thus, strategies such as changes in codon usage that aim solely at altering the expression level of the glycoprotein gene do not suffice to render a pathogenic rabies virus apathogenic and are not a viable and safe approach for attenuation of a pathogenic strain.     

Minigene-like inhibition of protein synthesis mediated by hungry codons near the start codon

Rare AGA or AGG codons close to the initiation codon inhibit protein synthesis by a tRNA-sequestering mechanism as toxic minigenes do. To further understand this mechanism, a parallel analysis of protein synthesis and peptidyl-tRNA accumulation was performed using both a set of lacZ constructs where AGAAGA codons were moved codon by codon from +2, +3 up to +7, +8 positions and a series of 3-8 codon minigenes containing AGAAGA codons before the stop codon. Beta-galactosidase synthesis from the AGAAGA lacZ constructs (in a Pth defective in vitro system without exogenous tRNA) diminished as the AGAAGA codons were closer to AUG codon. Likewise, beta-galactosidase expression from the reporter +7 AGA lacZ gene (plus tRNA, 0.25 microg/microl) waned as the AGAAGAUAA minigene shortened. Pth counteracted both the length-dependent minigene effect on the expression of beta-galactosidase from the +7 AGA lacZ reporter gene and the positional effect from the AGAAGA lacZ constructs. The +2, +3 AGAAGA lacZ construct and the shortest +2, +3 AGAAGAUAA minigene accumulated the highest percentage of peptidyl-tRNA(Arg4). These observations lead us to propose that hungry codons at early positions, albeit with less strength, inhibit protein synthesis by a minigene-like mechanism involving accumulation of peptidyl-tRNA.     

Bootstrap confidence intervals for adaptive cluster sampling

Consider a collection of spatially clustered objects where the clusters are geographically rare. Of interest is estimation of the total number of objects on the site from a sample of plots of equal size. Under these spatial conditions, adaptive cluster sampling of plots is generally useful in improving efficiency in estimation over simple random sampling without replacement (SRSWOR). In adaptive cluster sampling, when a sampled plot meets some predefined condition, neighboring plots are added to the sample. When populations are rare and clustered, the usual unbiased estimators based on small samples are often highly skewed and discrete in distribution. Thus, confidence intervals based on asymptotic normal theory may not be appropriate. We investigated several nonparametric bootstrap methods for constructing confidence intervals under adaptive cluster sampling. To perform bootstrapping, we transformed the initial sample in order to include the information from the adaptive portion of the sample yet maintain a fixed sample size. In general, coverages of bootstrap percentile methods were closer to nominal coverage than the normal approximation.     

Modulation of poliovirus replicative fitness in HeLa cells by deoptimization of synonymous codon usage in the capsid region

We replaced degenerate codons for nine amino acids within the capsid region of the Sabin type 2 oral poliovirus vaccine strain with corresponding nonpreferred synonymous codons. Codon replacements were introduced into four contiguous intervals spanning 97% of the capsid region. In the capsid region of the most highly modified virus construct, the effective number of codons used (N(C)) fell from 56.2 to 29.8, the number of CG dinucleotides rose from 97 to 302, and the G+C content increased from 48.4% to 56.4%. Replicative fitness in HeLa cells, measured by plaque areas and virus yields in single-step growth experiments, decreased in proportion to the number of replacement codons. Plaque areas decreased over an approximately 10-fold range, and virus yields decreased over an approximately 65-fold range. Perhaps unexpectedly, the synthesis and processing of viral proteins appeared to be largely unaltered by the restriction in codon usage. In contrast, total yields of viral RNA in infected cells were reduced approximately 3-fold and specific infectivities of purified virions (measured by particle/PFU ratios) decreased approximately 18-fold in the most highly modified virus. The replicative fitness of both codon replacement viruses and unmodified viruses increased with the passage number in HeLa cells. After 25 serial passages (approximately 50 replication cycles), most codon replacements were retained, and the relative fitness of the modified viruses remained well below that of the unmodified virus. The increased replicative fitness of high-passage modified virus was associated with the elimination of several CG dinucleotides. Potential applications for the systematic modulation of poliovirus replicative fitness by deoptimization of codon usage are discussed.     

Optimal codon identities in bacteria: implications from the conflicting results of two different methods

A correlation method was recently adopted to identify selection-favored 'optimal' codons from 675 bacterial genomes. Surprisingly, the identities of these optimal codons were found to track the bacterial GC content, leading to a conclusion that selection would generally shape the codon usages to the same direction as the overall mutation does. Raising several concerns, here we report a thorough comparative study on 203 well-selected bacterial species, which strongly suggest that the previous conclusion is likely an illusion. Firstly, the previous study did not preclude species that are suffering weak or no selection pressures on their codon usages. For these species, as showed in this study, the optimal codon identities are prone to be incorrect and follow GC content. Secondly, the previous study only adopted the correlation method, without considering another method to test the reliability of inferred optimal codons. Actually by definition, optimal codons can also be identified by simply comparing codon usages between high- and low-expression genes. After using both methods to identify optimal codons for the selected species, we obtained highly conflicting results, suggesting at least one method is misleading. Further we found a critical problem of correlation method at the step of calculating gene bias level. Due to a failure of accurately defining the background mutation, the problem would result in wrong optimal codon identities. In other words, partial mutational effects on codon choices were mistakenly regarded as selective influences, leading to incorrect and biased optimal codon identities. Finally, considering the translational dynamics, optimal codons identified by comparison method can be well-explained by tRNA compositions, whereas optimal codons identified by correlation method can not be. For all above reasons, we conclude that real optimal codons actually do not track the genomic GC content, and correlation method is misleading in identifying optimal codons and better be avoided.