Translational Model for Three Organisms

The following translational parameters were attributed to the analyzed genes: , coding sequence length in codons; , average number of transcripts in a cell; , average number of proteins produced from one molecule of transcript during its lifespan; , ribosome density in number of ribosomes attached to a transcript per 100 codons; , the absolute number of ribosomes on a transcript; , mean time required for translation initiation; , mean time required for translation elongation; , mean elongation time of one codon of a transcript; and , estimated mean lifetime of a transcript. Parameters , , , and are given in SI units.

The values of parameters , , , , , , and were attributed to 1738, 4470, and 7494 genes in E.coli, S.cerevisiae, and H.sapiens, respectively, which corresponds to the 42, 76, and 41% coverage of the genomes. Due to the accessibility of data, parameters and were determined only for subsets of analyzed genes, containing, respectively, 1574, 3425, and 6205 genes. The summary of quantitative measures of translation for the three organisms may be found in Table 1.

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Table 1. The summary of translational parameters calculated in the model.

https://doi.org/10.1371/journal.pone.0073943.t001

Web Service Implementation

All translational parameters for individual genes are presented on the Transimulation website. The database may be browsed or searched by the query engine. Simple searches may be performed by typing a single gene name, or a key word in the query window. More complicated queries, combining several gene names, key words, or values and ranges of translational parameters are also possible. The results page of an individual gene consists of a list of all the calculated translational parameters and an interactive simulation of translation.

The top part of the applet displays transcript coding sequence, which may be navigated or mutated with the help of appropriate buttons on the control panel. The current sequence may be downloaded as a fasta file anytime. The simulation starts by placing the ribosome active site on the initial codon and then moving it from one codon to another only if it has spent there the required amount of time for translation of the current codon and the subsequent codon is vacant. The successive ribosome attaches to the initial codon after a time interval equal to the translation initiation time. Ribosome collisions will not occur during simulation, if the original sequences are used, as only collision-free genes were retained in the database. Otherwise, ribosome blockage may take place. In such a case, the simulation stops and active sites of collided ribosomes are indicated by red exclamation marks. For easier identification of ribosome deceleration regions, plots of translation speed (in aa/sec) in relation to the original coding sequence are provided. To facilitate analysis, the plots may be smoothed by calculating translation speed over a sliding window of the size of 2, 5, 10, 20, 30 or 50 codons (see Figure 1).

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Figure 1. Translation speed plot generated by Transimulation.

An example plot of translation speed (in aa/sec) in relation to the coding sequence of one of the E.coli genes. To facilitate analysis, the plot was smoothed by calculating translation speed over a 10-codon sliding window. Similar plots for window sizes of 1, 2, 5, 10, 20, 30, and 50 codons are generated for all analyzed genes and sequences uploaded by the user.

https://doi.org/10.1371/journal.pone.0073943.g001

In addition, Transimulation allows to express any coding sequence in silico in one of the three studied organisms. To run simulation of ribosome movement, the time of translation initiation should also be provided by the user. Translation times of individual codons are those of the host organism. Most translational parameters are calculated based on the initiation time and the coding sequence. To calculate the number of proteins produced per mRNA – , mean lifetime of a transcript should also be provided. Additionally, translation speed plots (raw and smoothed) may be generated for the uploaded sequence. Finally, to facilitate more automatic analysis, the entire database of translational parameters, as well as translation times of individual codons, may be downloaded as flat files. Detailed manual for Transimulation users may be found on the website.

Agreement with Previous Studies

A detailed comparison of model results with other studies was shown previously for yeast [9]. However, as in this study we used different input data set for yeast mRNA degradation time [10], which is a key parameter for calculating , we repeated the comparisons of obtained protein abundances with experimental data. Similar but more detailed analysis for bacteria and humans was also performed.

At first, we examined the compatibility of our predictions with genome-wide, experimental measurements of protein levels for E.coli [11], S.cerevisiae [8], [12], and H.sapiens [13]. All scatter plots and distributions of log fold differences are presented in Figure 2 and S1, respectively. For H.sapiens the 95% confidence interval (CI) for the Spearman correlation coefficient is 0.65–0.68 (for sample size n = 3041), which means that our model explains 42–46% of the variability of protein levels measured experimentally. Globally, our predictions are overestimated by approximately one order of magnitude in relation to experimental studies. Next, we compared protein abundances in S.cerevisiae with those assessed experimentally by other groups [8], [12]. The obtained 95% CI for was 0.62–0.67 (n = 1778), and 0.52–0.80 (n = 60) for the Newman et al. and Gygi et al. data sets, respectively. Our predictions explain 38–45% and 27–64% of the experimental values’ variability in these data sets, and may be slightly shifted in relation to them, although the difference rarely exceeds one order of magnitude. For comparison, the 95% CI for calculated between these two experimental studies is 0.35–0.64 (n = 97), which corresponds to 12–41% of each other’s explained variability. For E.coli, the 95% CI for was 0.18–0.40 (n = 262), indicating that our model explains 3–16% of the variability of protein abundances measured experimentally. Again, there is a shift in values, but this time our protein levels are underestimated; for some genes this shift may be serious (several orders of magnitude), as may be seen from the long left tail of the log fold differences distribution (Figure S1). For explanation of this fact, see Discussion.

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Figure 2. Calculated protein abundance vs experimental studies.

Correlations between protein abundances calculated in our model (as times ) and those obtained in experimental studies [8], [11]–[13]; n – sample size, – Spearman correlation coefficient and its 95% confidence interval.

https://doi.org/10.1371/journal.pone.0073943.g002

Furthermore, many of the obtained cell-wide parameters of translation can be compared with other quantitative studies. For instance, according to our model the global ribosome density calculated over the entire E.coli transcriptome equals 3.46 ribosomes per 100 codons. Assuming that a ribosome covers 10 codons, the length of average gap between ribosomes equals ∼19 codons, which corresponds to an earlier report [14], claiming 14–28 codons between adjacent ribosomes. Additionally, the average translation rate for bacteriae cells was estimated at 12–21 [14], and 15 aa/sec [15], while our model predicts 8.4 aa/sec. Our mean transcript lifetime of 7.5 min for E.coli agrees well with previous estimates of 5.87 min ± 34 s [16] and 5–10 min [17]. Besides, Open WetWare web page (http://openwetware.org, accessed Jan 2013) provides a list of E.coli statistics, which generally confirm our calculations of: transcript copy number per gene (2–3 according to Open WetWare vs. 1.7 in our model [median]); translation initiation time (20–30 vs. 15 s in our model [median]); the number of proteins produced from one transcript (40 vs. 28 [median] and 48 [mean] in our model). There is a discrepancy in the mean number of proteins produced from a gene (1000 vs. 45 [median] and 205 [mean]). Other studies also claim that the total number of proteins in a bacterial cell is ∼2.4 mln [18], while our calculation (sum of times over all analyzed genes) gives only ∼300,000. The origins of all the discrepancies are analyzed in Discussion.

In HeLa cells, the global translational rate estimated by the model is ∼11 aa/sec. Previous studies reported 6 aa/sec for human apolipoprotein B [19], 0.74 aa/sec for rabbit hemoglobin [20], 5 aa/sec for chick ovalbumin [21], and an average translation rate of 7.3 aa/sec in cockerel liver [22]. Moreover, according to reference [23], the entire proteome of a mammalian cell contains about 8e9 molecules, while our model predicts 6e9 proteins per cell. The distribution of protein abundances is also in accordance with this report, claiming variation in protein levels from less than 100, to 1e8 molecules, depending on their function. In our model, the number of proteins produced from a gene ( times ) is between 127 and 1e8 molecules per cell, with median 230,000 and standard deviation 3.3e6.

Case study: Comparison of Translation in Three Organisms

To demonstrate the applicability of Transimulation to answering biological questions we used its data to estimate conservation of translational parameters between evolutionary related genes. By taking advantage of the Inparanoid database [24] (accessed Jan 2013), we prepared a list of 69 orthologous genes present in E.coli, S.cerevisiae and H.sapiens genomes, for which translational parameters can be found on the Transimulation website (Table S1). We measured the agreement between parameters values for all possible pairwise comparisons, by calculating 95% confidence intervals CI for the Spearman correlation coefficient . All results, as well as three-dimensional scatter plots, are provided in Figure S2.

The closest agreement, yet still relatively small, was found for the transcript copy number . For intra-species comparisons, all correlations were positive, with lower CIs limits between 0.13–0.29, and upper CI limits between 0.55–0.65, indicating that the percent of explained variability of mRNA levels is in the range 2–42. Although this is not much, and could result from data noise, we must not forget that the analyzed species are very distant, and stronger signals are hardly expected. No coherent picture emerges from comparisons of parameters , , , , and , as obtained confidence intervals are too ambiguous to decide on correlation sign, thus precluding any further discussion. The only exception is the case of the yeast-human comparison for parameters and , for which some positive correlations were found. Here again, the signal is weak, possibly explaining as little as 4–5% of the values variability. The number of ribosomes attached to a transcript correlates better, with lower CI limit of 0.43, corresponding to at least 18% of the explained variability. However, this is the result of strong conservation of orthologs’ sequence length , which significantly affects the calculations of . This influence is also visible in elevated CIs for the remaining intra-species comparisons of .

Translation elongation time seems strongly conserved, with correlation CI lower limits ranging from 0.7 to 0.83, indicating that at least 49% of values variability could be explained. Nevertheless, this is again due to conservation of , the main determinant of total elongation time. In particular, the inter-species comparisons for the samples of 69 genes show very strong correlations between and , with above 0.83 (yeast), 0.96 (bacteria), and even 0.99 (humans). Furthermore, this is confirmed by unambiguous correlations of , mean elongation time of one codon of a transcript, suggesting that in case of evolutionary related genes of similar sequence (and thus sequence length) any variability of elongation times of individual codons (or codons substitutions, insertions, and deletions) has negligible effect on total elongation time of the transcript. The differences in elongation times of individual codons seem too small to significantly affect for sequences of similar length. Hence, it should not be surprising that the intra-species comparison of mean elongation times of 61 sense codons (all measured at 37°C) results in very weak (if any) positive correlations. However, this may also be explained by the independent adaptation of species to the changes in tRNAs pool in the cell.

Taken together, our results suggest rather modest conservation of transcript copy number in orthologs. We cannot exclude the possibility that ribosome density and initiation time is also slightly conserved, although it could not be confirmed by comparisons with E.coli. Possibly, the evolutionary distance between bacteria and analyzed eukaryotes is too large to detect such a weak signal. We could not detect any conservation of mean transcript lifetimes and the number of produced proteins per transcript, which may stem from the fact that in the course of evolution many of the analyzed genes duplicated, gained or lost function. In consequence, their stoichiometry in the cell may be very distant from that in the theoretical common ancestor of these three species. Finally, the observed conservation of total elongation time of orthologs should rather be due to similar sequence length of analyzed genes.

Computational Model of Translation

The model used to calculate the translational parameters presented in our web service has been described in detail previously [9]. The majority of the input data and other variables required for the model were found in the Bionumbers database [28], and are presented in Table 2. All translational parameters for yeast, except and , were taken directly from Table S1 of [9]. Below, we briefly summarize the calculations, along with some details on data sets parsing for the remaining organisms. More thorough derivation of the equations may be found in our previous work [9].

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Table 2. Summary of data sets and variables used as an input of the model.

https://doi.org/10.1371/journal.pone.0073943.t002

Coding Sequences

Coding sequences of the analyzed organisms were downloaded from the web resources shown in Table 2. Our reference genomes were the same as those used in the ribosome profiling analysis of the species, i.e. NC_000913 for E.coli, and hg18 for humans.

Codon Elongation Times

Mean elongation times of individual codons of E.coli were taken directly from [29], and for yeast from [9]. For humans, we obtained them as described in [29]. In short, the average time to add an amino acid coded by the codon to the nascent peptide chain was calculated as stated in [29], namely:(1)where is the average time to insert an amino acid from a cognate aa-tRNA, and and are the average time delays caused by the binding attempts of near- and non-cognate aa-tRNAs, respectively. Values of , and can be calculated at any given temperature, as shown by [29]. In our analysis we used the same temperatures at which the cells were grown in the ribosome profiling experiments: 30°C for yeast, and 37°C for E.coli and humans. In the above equation and stands for two tRNA competition measures, being the quotients of the sums of arrival frequencies of near-cognates vs. cognates and non-cognates vs. cognates, respectively. For each codon we determined its cognates, near- and non-cognates, based on data sets on tRNA specificities listed in Table 2. We assume that all sense codons have one or more cognate aa-tRNA and varying numbers of near-cognates. Near-cognates are defined as having a single mismatch in the codon-anticodon loop in either the 2nd or 3rd position. Since some cognate tRNAs have a mismatch in the 3rd position, these tRNAs are excluded from the set of near-cognates [30]. The arrival frequency of the aa-tRNA molecule is defined as in [29]:(2)where is the diffusion coefficient, is the number of molecules in a cell, is the molecule size in m, and is the average cell volume in m. The values of for all aa-tRNAs were taken directly from [29]. As this value depends only on the accepted amino acid, we assumed that the difference in size between E.coli and other species’ tRNAs is negligible. For humans the diffusion coefficient of the tRNA(Cys) was used for the selenocysteine isoacceptor tRNA(Sec). The levels of tRNA molecules in a cell, as well as their decoding specificities, were taken from sources given in Table 2. If necessary, the relative abundances were transformed to absolute values assuming the total number of tRNAs listed in Table 2. The values of used previously [29] were determined separately for individual E. coli aa-tRNA molecules [31]. As we are not aware of any similar reports for other analyzed organisms, we decided to use for other species’ codons, which is the mean of the E. coli values. Average cell volumes for E.coli, yeast and humans were taken directly from the references in Table 2. Mean codon elongation times for all three species may be downloaded as flat files from the Transimulation web page, and parameters , and are presented in Table S2. The list of cognate and near-cognate tRNA for each codon, as well as the measures and , may be found in Table S3.

Transcript Abundance

The levels of mRNA molecules were taken directly from the references in Table 2. If necessary, the relative abundances were transformed to absolute values assuming the total number of mRNAs given in Table 2 and complete coverage of the transcriptome by the reference study.

Ribosome Density

The average number of ribosomes attached to a transcript – , as well as the ribosome density (the number of attached ribosomes per 100 codons), were determined on the basis of genome-wide ribosome profiling data, as stated in Table 2. For human and yeast, genes that did not have either ribosome or mRNA footprint counts at all, or their sum was below 128, were excluded from further analysis. As the E.coli data set does not provide information on mRNA counts, only genes with less than 100 ribosome footprint counts in at least one repetition were excluded. When transforming footprint counts into ribosome density for E.coli, one obstacle cannot be ignored – the fact that typically E.coli expresses ∼600 genes at a time from the pool of ∼4000 [15] and transcript turnover is very rapid [16], [17]. The ribosome profiling data provide information for ∼3000 genes, which means that it concerns bacterial cells at many possible stages. The key parameter for ribosome density calculation is the sum of all footprints from the experiment, which is assumed to correspond to the total number of footprints in a cell. In bacteria the sum calculated over all ∼3000 analyzed genes would be seriously overestimated. To overcome this problem, we estimated it by finding the mean of 1000 sums calculated over 600 genes, sampled without replacement from the pool of 3331 genes of known footprints count. For all species the total number of ribosomes required for calculations of was taken from the references in Table 2, and it was assumed that 85% of ribosomes present in the cell actively participate in translation [32], [33]. Assuming that a ribosome covers about 10 codons [34], only transcripts with 10 were retained.

Other Translational Parameters

The average elongation time of a transcript was calculated as the sum of mean elongation times of its codons. Transcript mean elongation time of one codon was calculated as , where stands for sequence length in codons. The translation initiation time was calculated as the quotient of and the number of ribosomes attached to a transcript – , as discussed previously. Mean mRNA lifetimes were taken from the references listed in Table 2. The expected number of proteins produced from a transcript during its lifespan was calculated as the quotient of the mean lifetime and translation initiation time . Using the simulation of ribosome movement on a transcript and calculated parameters, we reduced the final data set to the transcripts on which ribosome queuing does not occur. We excluded 89, 151 and 194 transcripts from E.coli, yeast and human data sets, respectively.