Grantham et al. (1980) highlighted the unequal usage of synonymous codons among different genes and genomes in a phenomenon currently known as codon usage bias (CUB). Thenceforward, scientists were investigating the effect of synonymous mutations on the efficiency/accuracy of protein translation and several biological processes ranging from RNA processing to protein folding and their potential consequences on the overall performance and evolution of living organisms (Chamary et al., 2006; Plotkin and Kudla, 2011). Codon usage is positively associated with the analogous tRNA in a species—the tRNA pool determines the available amino acid used during the protein extension process. Therefore, protein expression and translation efficiency are highly associated with CUB (Karlin et al., 2001; Gustafsson et al., 2004). Accordingly, codons with high occurrence in a gene (putative optimal codons) improve the protein translation rate, and rare codons will cause a reduction in the translation and might cause translation errors (Ikemura, 1981).

In biotechnology studies, heterologous expression was applied to assemble vaccines and pharmaceuticals (Han et al., 2010; Liu et al., 2018). Codon optimization was proposed to increase heterologous gene expression (Quax et al., 2015; Brandis and Hughes, 2016; Fu et al., 2020). Many studies reported the success of the codon optimization approach to upregulate gene expression up to 1,000-fold (Quax et al., 2015). Several software tools are used for codon optimization and are patented to serve commercial purposes such as GenSmart Design (https://www.genscript.com/gene-and-plasmid-construct-design.html) and GENEWIZ (https://www.genewiz.com/en-GB/Public/Services/Gene-Synthesis/codon-optimization). A number of codon optimization algorithms are not open-source (Satya et al., 2003; Huang et al., 2021) or should be requested from the authors (Fuglsang, 2003). Regardless of their availability, many of those protein expression optimization software tools are based on the tRNA adaptation index (tAI) (Gould et al., 2014; Watts et al., 2021; Raguin et al., 2023) and codon adaptation index (CAI) (Fu et al., 2020). Many indices were developed to measure the degree of preference for the unbalanced use of codons. Some are codon-specific such as relative synonymous codon usage (RSCU), and others are gene-specific such as the effective number of codons (ENc) (Wright, 1990; Sun et al., 2013) and CAI (Sharp and Li, 1987). A relatively new index named tAI was introduced by dos Reis et al. (2004) to become a formal measure for CUB associated with translational selection. The tRNA presents a complementary anticodon for an amino acid to be incorporated into the growing polypeptide chain during the translation process. The codon–anticodon interactions at the first two codon positions are governed solely by canonical (Watson–Crick) base pairing rules, unlike the third codon position at which non-canonical (wobble) base pairing also occurs (Crick, 1966). The tAI considers weights for canonical and wobble interaction efficiencies between codons and tRNA molecules. To compute the tAI, first, the absolute adaptiveness value (W _i ) for codon i is calculated by the following equation: W i = ∑ j = 1 n j 1 − S i j t G N C i j , (1)

where n _j is the number of tRNA isoacceptors that can recognize the ith codon, S _ij is the codon–anticodon coupling efficiency having values ranging from 0 (perfect interaction) to 1 (weak interaction) (dos Reis et al., 2004), and tGNC _ij is the gene copy number of the jth anticodon that can recognize the ith codon.

Then, each W _i is normalized to the maximum W _i value to obtain the relative adaptiveness value (w _i ). Finally, the tAI of a gene can be defined as the geometric mean of the w _i values of its codons (dos Reis et al., 2004): t A I g = exp 1 O t o t ∑ i ∈ I log   w i , (2) where O _tot is the frequency of the total codons.

The S _ij weights inferred by the original tAI (otAI) implementation were based on optimizing the correlation between tAI (Eq. 1) and gene expression levels in Saccharomyces cerevisiae using the Nelder–Mead method under the assumption that highly expressed genes contain codons with higher adaptation to the tRNA pool (driven by the force of translational selection). In a study by Dana and Tuller (2014), two problems are associated with the original tAI implementation. First, it depends on gene expression information, often unavailable for many organisms (especially novel ones). Second, generated weights were specific for Saccharomyces cerevisiae. They suggested the possibility that wobble interaction efficiencies shall differ significantly among genomes from different domains. So, it would not be plausible to use the weights specifically for Saccharomyces cerevisiae to compute the tAI of other organisms. Consequently, they developed the species-specific tAI (stAI) (Sabi and Tuller, 2014) to solve these problems.

The inferred stAI weights are based on optimizing the correlation between the tAI (Eq. 1) and a CUB index, namely, directional codon bias score (a modified version of relative CUB (Oymondal et al., 2009)) using the hill climbing algorithm under the assumption that highly expressed genes have higher adaptation to the tRNA pool and higher CUB (Sabi and Tuller, 2014). This eliminates the need for additional gene expression data and generates weights specific to the tested organism, indicating the value of stAI in tAI computation, especially for non-fungal species. However, two limitations in the stAI are as follows: 1) using the hill climbing optimization method by which only local maxima can be reached and often gets stuck in ridges and plateau scenarios (Thengade and Dondal, 2012); hence, the best set of S _ij weights may not be obtained even after using different starting positions (random restart) (Russell and Norvig, 2010; Yang, 2014); 2) the outperformance of the original tAI over the stAI in predicting the protein abundance (PA) of fungal organisms (Sabi and Tuller, 2014).

Here, we introduce a novel approach for tAI computation, namely, genetic tAI (gtAI), to solve the problems associated with the stAI, which affect its performance. The gtAI uses a genetic algorithm to reach the global maximum (best set of S _ij weights), solving the issue of obtaining a meaningful set of S _ij weights for each organism. It also utilizes robust CUB indices (ENc and RSCU) different from the directional codon bias score (DCBS) employed by the stAI.

The tAI is a formal measure of the force of translational selection. It has been widely employed to investigate fundamental questions related to gene expression, molecular evolution, and virus–host adaptation (Sharp et al., 2005; Man and Pilpel, 2007; Goodman et al., 2013; Pechmann and Frydman, 2013; Sabi and Tuller, 2014). Due to its importance, we were motivated to improve its performance by solving the issues of previous methods used for its calculation. We evaluated our proposed method mainly by examining whether it correlates better with other well-established codon usage indices. In addition, it shows a better association with empirical PA data.

The CAI is a gene-specific CUB index (Sharp and Li, 1987). Many studies suggested that the CAI is a good predictor of gene expression at mRNA and protein levels and has been used in many studies as a reference index to compare new indices and methods (Carbone et al., 2003; Sun et al., 2013; Fu et al., 2020). Accordingly, we conducted a comparative analysis on 12 model organisms (Supplementary Table S1) to evaluate the performance of the gtAI method compared to the original tAI and stAI (Supplementary Tables S2–S5) by examining whether it correlates better with the CAI using Spearman’s rank correlation analysis. The gtAI managed to outperform both methods by exhibiting a stronger significant correlation in 9 out of 12 model organisms with the CAI.

Attempting to explain the reason behind the better association of the stAI with the CAI than the gtAI in F. placidus, V. cholera, and C. elegans revealed a notable conclusion. These three organisms showed the highest ENc (low CUB) average value within their domains. For example, the average ENc value of the reference set for F. placidus was 44.8, while in H. mukohataei and M. jannaschii, the ENc values were 34.25 and 37.91, respectively. The same trend was observed in the bacterial group, as the average ENc value for V. cholera was 41.83, 39.08 for E. coli, and 37.08 for N. meningitidis. For non-fungal eukaryotes, C. elegans exhibited a 42.02 average ENc value, while 38.69 for D. melanogaster. This shows one limitation in our approach which can be attributed to organisms with overall weak CUB. It slightly influenced the result of the gtAI leading to the better correlation of stAI in these organisms. Furthermore, insights into the relation between GC content and gtAI performance have revealed that the change in GC content could not explain the slight outperformance of the stAI over the gtAI in terms of correlation with the CAI except in archaeal genomes. To embark on, in non-fungal eukaryotes, though C. elegans has an average GC content of 35.4%, indicating a possible strong bias against GC-rich codons, it showed an overall relatively weak bias (ENc = 42.02) which resulted in the slight underperformance of gtAI compared to stAI. Additionally, though D. melanogaster has a relatively higher GC content of 42.0% (closer to 50%), indicating relatively weaker bias, it showed an overall relatively stronger bias (ENc = 38.69) than C. elegans. Meanwhile, in Archaea, it is notable that the change in their overall bias is consistent with their deviation from the 50% GC content. In other words, the archaeal genome that showed an underperformance of gtAI (F. placidus) has an average GC content of 44.1% which is the closest to 50% compared to the other two archaeal genomes of 31.4% and 65.5%, as well as the highest ENc value of 44.8 compared to the other two of 34.25 and 37.91. Without regard to this limitation, the results (Table 1) suggest that the gtAI method performance was better for S _ij value optimization, giving a more reliable tAI value that better demonstrates the effect of translational selection.

One can argue that the correlation between the gtAI and CAI might be inflated due to using the same reference set of genes. Hence, we conducted two more analyses to test it. In the first one, we obtained multiple random samples of CAI and the three tAI indices’ values and performed Spearman’s rank correlation analysis between each of them with the CAI. The results remained the same and agreed with our conclusion as the gtAI showed a stronger correlation with the CAI than the stAI in the same nine organisms. In addition, a higher correlation with the CAI than the original tAI in the four fungal organisms was shown. In the second analysis, we investigated whether gtAI correlates better with another CUB index that is independent of using a reference set of genes in its calculation, namely, SCUO (to exclude the reference set parameter). The results also revealed a stronger gtAI association with SCUO, further confirming that the correlation between the gtAI and CAI is not inflated nor affected by the reference set of genes.

In conclusion, our gtAI method can solve the query of S _ij value optimization and effectively estimate the tAI values while overcoming the limitations observed in other implementations. Performance evaluation showed that the gtAI method performed better than the original tAI and stAI by exhibiting a stronger correlation with the CAI and SCUO. It has also improved the prediction of PA compared to the stAI and CAI. The reproducibility of the genetic algorithm employed by the gtAI was tested and revealed its reliability in reaching the best solution in complex optimization problems. The Wi values generated by the gtAI correctly reflect the evolutionary proximity between organisms from different domains of life. Indeed, one significant advantage of CUB-dependent tAI computation methods (i.e., gtAI and stAI) over the original tAI is the lack of neediness for external information such as gene expression data or mRNA levels (which are often unavailable for most genomes). We believe that the gtAI will allow for obtaining higher quality tAI results used to draw conclusions about the force of translational selection acting on genes in related studies.