Measuring translation-initiation rates.

To derive an analytical expression relating the translation-initiation rate to the experimental observable of ribosome density along a transcript we assume steady state conditions, meaning that the ribosome flux at each codon position is equal to the rate at which fully synthesized protein molecules are released. Thus, for any transcript i, we have: (1) where F(1, i) is equal to the flux of ribosomes initiating translation at the start codon, F(j, i) is the flux of ribosomes moving from codon position j to (j + 1) on copies of transcript i, N_c(i) is the number of codons in the transcript, and F(N_c(i), i) is the flux of ribosomes terminating translation from the stop codon. In our modeling, the position of a ribosome on a transcript is defined by its A-site location.

Let be the number of codon positions that a ribosome covers on a transcript. A ribosome typically covers 10 codon positions and hence ℓ = 10 with the A-site of the ribosome located at the sixth codon position in this segment [15]. A ribosome initiating translation will, therefore, cover codon positions 1 through 6 in the coding sequence, with the other portion covering part of the transcript’s 5′ UTR. It follows then that a ribosome translating any of the first codons will prevent a new ribosome from initiating translation by physically blocking the first six codon positions of the transcript. Thus, the ribosome flux at the start codon is (2) where α(i) is the initiation rate in the absence of any ribosome at the first codon positions, and ρ(k, i) is the average ribosome occupancy at the k^th codon position of the transcript [28]. Note well, Eq (2) assumes that the ρ(k, i)s for the first ten codon positions are independent of each other, and is therefore a first-order approximation of an exact solution and thus Eq (2) ignores higher order terms of α(i) [28]. This assumption may introduce inaccuracies in the calculation of F(1, i) for large α(i)s. Polysome profiling experiments [29] and computer simulations of protein synthesis [21], however, suggest that most S. cerevisiae transcripts are translated in the regime of low average ribosome density. As a consequence, ignoring higher order terms of α(i) in Eq (2) provides a reasonable estimate of F(1, i). Under a mean-field assumption [30], the ribosome flux at the j^th codon position for copies of transcript i can be written as (3)

In Eq (3), ω(j, i) is the intrinsic translation rate of the j^th codon position in the transcript (i.e., the rate that would be observed in the absence of any other ribosomes), and is the conditional probability that given that a ribosome is at the j^th codon position there is no ribosome at the codon position.

We used Eqs (1), (2) and (3) to derive (see S1 Text) the following expression for translation-initiation rate (4) where is the average ribosome density per codon on the i^th transcript, and 〈T(i)〉 is the average time a ribosome takes to synthesize a full-length protein from the transcript. Eq (4) can measure the translation-initiation rate provided 〈T(i)〉, 〈ρ(i)〉 and the ρ(j, i)s are known. We calculated 〈ρ(i)〉 and ρ(j, i) from ribosome profiling, RNA-Seq and polysome profiling data, and 〈T(i)〉 using a scaling relationship [31] between protein synthesis time and CDS length. Full details for determining these parameters are provided in S1 Text.

Measuring the average translation elongation rate across a transcriptome.

In ribosome run-off experiments performed on eukaryotic cells translation-initiation is inhibited at time point t = 0 using the drug harringtonine [26]. This causes ribosomes to accumulate at start codons and thereby block new translation-initiation events. At time t = Δt, the cells are treated with cycloheximide, which stops translation elongation by the ribosomes. The experiment is repeated at different Δt values. A meta-gene analysis of ribosome profiles [32] is then obtained from each run-off experiment and used to quantify the depletion of ribosome density across the transcripts as a function of time, allowing the transcriptome-wide average elongation rate to be measured [26].

To model this non-steady state data, we assume that ribosome movement along transcripts is a form of mass flow along one dimension–a reasonable assumption given that ribosomes can move only in one direction along a transcript. In this case, a natural way to describe this phenomenon is the continuity equation (5) which equates the decrease in density of a substance (ρ, the ribosome occupancy in our case) over time, t, with the outward flux J of that substance from a particular region of space. The equality with zero in Eq (5) is a manifestation of conservation of mass. In the ribosome run-off experiment this corresponds to a depletion of ribosome density along a segment of a transcript as ribosomes move out of that region with rate J, and are not replenished by new ribosomes since initiation was halted at time t = 0.

According to the definition of divergence, ∇ · J is the rate at which ρ exits from a given closed space [33]. For a system composed of L codons along a transcript that are being translated by ribosomes, (see S1 Text, Eq. (S14)). Substituting this value of ∇ · J into Eq (5) and then integrating over t from 0 to Δt yields (6) where ρ(t = Δt, L) is the average ribosome density of the transcriptome within the first L codon positions of a sample at run-off time Δt. is the average time at which equals zero. in Eq (6) is calculated using the ribosome run-off data. Explicit details of this calculation are provided in the S1 Text.

We inserted the relative average ribosome density ρ(t = Δt, L)/ρ(t = 0, L) obtained from Eq (S16) into Eq (6) and plotted this against Δt. By fitting this data to a straight line we determined τ(L), the time at which ρ(t = Δt, L)/ρ(t = 0, L) equals zero. τ(L) is, therefore, the time at which the last translating ribosomes have crossed the L^th codon position, on average. We calculated τ(L) in this way for different L values up to the minimum L value at which ribosome density depletion no longer occurs even at the longest run off time in the experiment. The average transcriptome-wide elongation rate 〈ω〉 is therefore equal to (7)

Measuring individual codon translation rates.

To derive a mathematical expression for extracting codon translation rates from ribosome profiling data we assumed steady state conditions in which the flux of ribosomes at each codon position is equal to the rate of protein synthesis (8)

In Eq (8), and τ(j, i) are, respectively, the steady-state number of ribosomes and the average translation time of the j^th codon position within copies of transcript i in a given experimental sample. The mean total time of synthesis 〈T(i)〉 of transcript i is, by definition, equal to (9)

Solving Eqs (8) and (9) for τ(j, i) (see derivation in S1 Text) yields (10)

As is the convention in the field [34], we assume that ribosome profiling reads at the j^th codon position of transcript i, c(j, i), are directly proportional to . This relationship can be expressed as (11) where a_j,i is a constant of proportionality. a_j,i values have not been experimentally measured, but they are commonly assumed to be constant for all codon positions in a single experiment [34]. That is, a_j,i = a_i for all i and j. Using Eq (11) with a_j,i = a_i in Eq (10) yields (12)

Eq (12) indicates that we can determine the individual codon translation rates from ribosome profiling reads provided we know the average total synthesis time of the transcript. Eq (12) can be connected to the expression for normalized ribosome density, derived in the SI of Ref. [16], where is the normalized ribosome density and is expressed as a function of c(j, i)s. Eq (12) is also related to a metric used in the simulations of Ref. [14] to estimate the codon translation rates. It is important to note that τ(j, i) is the actual codon translation time, which includes the time delay caused by ribosome-ribosome interactions and is distinct from the intrinsic translation rate of a codon ω(j, i). τ(j, i) is equal to the inverse of [35].

In silico validation of our methods.

As a first step to test the accuracy of the measured translation rates from Eqs (4), (7) and (12), we applied them to artificial S. cerevisiae ribosome profiles generated by kinetic Monte Carlo [36] and Gillespie simulations [37] in which all of the underlying rates are known (see Methods). If our analysis methods are accurate then a necessary condition is that they reproduce these rates from the simulated profiles. We applied Eq (4) to the simulated, steady-state ribosome profiling data and find that it quantitatively reproduces the initiation rates used in the simulations (Fig 1A, slope = 0.97, R² = 0.84 and p-value < 10⁻⁶⁰). We applied Eq (7) to the non-steady state ribosome run off profiles of S. cerevisiae (Fig 2A and 2B) and find that it accurately measures the transcriptome-wide average translation rate. Specifically, our method measures the transcriptome-wide average elongation rate at 3.8 AA/s against the real average elongation rate of 4.2 AA/s. Note well, that as predicted by Eq (6), we also observe a linear decrease in as a function of time (S1A Fig). Finally, we applied Eq (12) to the steady-state ribosome profiles and find that the individual codon translation times are accurately measured by our method (Fig 3, median R² = 0.96 and median slope = 1.00). Thus, the analysis methods we have created can in principle accurately capture the translation rate parameters.

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Fig 1. Eq (4) accurately determines the translation-initiation rate from simulated S. cerevisiae ribosome profiles and its application to experimental data.

(A) Translation-initiation rates determined by applying Eq (4) to simulated ribosome profiling data are plotted against the actual initiation rates used in the simulations. These initiation rates were calculated using Eq (S10) for the average protein synthesis times. (B) Same as (A) but the average protein synthesis times were measured from our simulations of the translation process. The solid lines in (A) and (B) are the lines of the best fit. (C) The distribution of in vivo translation-initiation rates measured by applying Eq (4) to experimental data involving 1,287 S. cerevisiae high coverage transcripts.

https://doi.org/10.1371/journal.pcbi.1007070.g001

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Fig 2. Measuring average elongation rate by applying Eq (7) to in silico and in vivo ribosome run-off data.

(A) Normalized average ribosome read density (), Eq. (S15), calculated from simulated ribosome run-off experiment is plotted as a function of codon position for run-off times of 0, 5, 10, 15, 20, 25 and 30 s⁻¹ with black, red, blue, cyan, pink, yellow and green data points, respectively. (B) The average time taken to fully deplete the normalized average ribosome read density within a window of the most 5′ codons positions in S. cerevisiae transcripts are plotted against the most 3′ codon position of the window. (C) Normalized average ribosome read density, calculated from in vivo run-off experimental data reported in Ref. [26], are plotted as a function of codon position for the run-off times of 0, 90, 120 and 150 seconds with black, red, blue and cyan data points, respectively. (D) The average time taken to fully deplete the normalized average ribosome read density within a window of the most 5′ codons positions in mouse stem cells transcripts are plotted against the most 3′ codon position of the window. The negative intercept reflects the time taken by harringtonine to engage with ribosomes.

https://doi.org/10.1371/journal.pcbi.1007070.g002

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Fig 3. Eq (12) accurately determines codon translation times from simulated ribosome profiles.

(A) Average translation time of a codon in YER009W S. cerevisiae transcript is plotted as a function of its position within the transcript. The true codon translation times in the simulations are plotted as green boxes, blue and black data points are the translation times measured using Eq (12). Blue data points were calculated using the average protein synthesis time measured from the simulations and relative ribosome density calculated using a large number of in silico ribosome profiling reads. Black data points were calculated using the average protein synthesis time estimated from the scaling relationship (Eq. (S10)) and the relative ribosome density calculated from the in silico reads which were equal to the reads aligned to the same transcript in the experiment [16]. (B) Measured codon translation times, plotted with black and blue data points in (A), are plotted against true codon translation times in the simulations in the top and bottom panel, respectively. (C) Probability distribution of the R² correlation between the true and calculated codon translation times for the 85 S. cerevisiae transcripts. (D) Probability distribution of the slope of the best-fit lines between the estimated and true codon translation times for the 85 S. cerevisiae transcripts. The high R² in (C) and median slope of 1.00 in (D) indicate that Eq (12) can, in principle, accurately measure absolute rates.

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There are several points worth noting concerning these tests. First, the rates used in the simulation model are realistic, having been taken from literature values [10,38]. Second, the depth of coverage in the simulated ribosome profiles is in the same range as experiments, e.g., having 26 million reads arising from 1,388 different coding sequences [16]. Third, Eqs (4) and (12) require knowledge of the average synthesis time of a protein, which is experimentally difficult to measure. Therefore, in the above analyses we used the approximation that the average synthesis time of a protein is proportional to the number of codons in its transcript, multiplied by the transcriptome-wide average codon translation time (Eq. (S10)) [26,31]. However, when we use the actual synthesis time of each transcript we achieve even better agreement between the estimated and true translation initiation rates (Fig 1B, slope = 0.99, R² = 0.95 and p-value < 10⁻⁶⁰). Similarly, when we increase our read coverage from 7.1 million to 35.5 billion reads and use the exact synthesis time of a protein, R² between the estimated and true codon translation rates goes to > 0.99. Thus, our model is reasonably accurate when approximate protein synthesis times are used (Eq. (S10)) and the coverage is similar to typical experiments, and highly accurate when the exact synthesis time is used and coverage is high.

Ribosome profiling data tend to exhibit a higher ribosome density near the start codon as compared to the rest of the transcript [16]. This feature might bias the in vivo measurement of initiation rate using our method, as Eq (4) is a function of the ribosome density of the first 10 codon positions. To assess the effect of this feature on the accuracy of our method we created in silico ribosome profiles by running synthesis simulations in which the translation rates of the first 100 codons were 50% slower for all S. cerevisiae 1,388 transcripts. This artificial decrease in codon translation rates introduced more ribosome density near the start codon. Using these in silico ribosome profiles, we find that Eq (4) still recapitulates the initiation rates with a similar level of accuracy as before (S2 Fig, R² ≥ 0.85). Thus, higher ribosome density near the start codon does not substantially affect the accuracy of our method. Our simulations do not account for other possible biases associated with ribosome profiling experiments, including sequencing amplification biases [39]. Thus, the accuracy of our model as determined from these in silico ribosome profiles might represent an upper bound to the accuracy on actual in vivo profiles with similar sequencing depth.

Measuring the initiation rate from experimental data.

We next applied Eq (4) to in vivo ribosome profiling and RNA-Seq data from S. cerevisiae reported in Ref. [16]. Calculation of the translation-initiation rate for a transcript requires knowledge of the average time a ribosome takes to synthesize the protein (〈T(i)〉) and the average occupancies of the first ten codon positions (ρ(j, i)). The average protein synthesis time was calculated using the scaling relationship (Eq. (S10)) where the transcriptome-wide average codon translation time was set to 200 ms as reported in the literature [40,41] (see S1 Text). ρ(j, i)s were calculated from Eq. (S9) using the ribosome profiling and RNA-Seq data from Ref. [16] and polysome profiling data from Ref. [42]. We then inserted these arguments into Eq (4) to calculate the translation-initiation rates for 1,287 S. cerevisiae transcripts that meet the filtering criteria (see Methods) and for which polysome profiling data is available. We find the translation-initiation rates vary from as low as 5.8 × 10⁻² s⁻¹ (5^th percentile) to as high as 0.24 s⁻¹ (95^th percentile) with the most probable rate being 0.1 s⁻¹ (Fig 1C and S1 File). These translation-initiation rates are significantly lower than the average elongation rate in S. cerevisiae which is consistent with previous studies indicating that initiation is the rate limiting step in translation [21]. The distribution of translation-initiation rates measured using Eq (4) is very similar to the distribution reported in Ref. [10], which was obtained using polysome profiling data.

To test the reproducibility of these results we calculated in vivo translation-initiation rates using the ribosome profiling and RNA-seq data measured by Nissley et al. [43] and polysome profiling data in Refs. [29,42]. These in vivo initiation rates are reported in the S1 File. We have found a statistically significant correlation between the initiation rates measured from the Weinberg et al. [16] and Nissley et al. [43] data sets (S3 Fig). The Pearson correlation between them was 0.53 (P = 10⁻⁴⁶) and 0.31 (P = 4 × 10⁻¹⁵) when polysome profiling data of Mackay et al. [42] and Arava et al. [29] were used, respectively. We have also compared these in vivo initiation rates with the ones measured in the study of Dao Duc and Song [14] and found a statistically significant correlation between them with Pearson r varying from 0.51 to 0.80 (P < 10⁻²⁴), depending upon the data sets used (S4 Fig).

Reproducing known correlations with initiation rates.

Next, we tested whether our measurements reproduce previously reported correlations between initiation rates and CDS length, sequence context upstream and around the start codon, folding energy near the 5′ cap of mRNA molecule, and protein copy number. Initiation rates can depend on CDS length because the shorter a transcript, the more probable the termini will be in close proximity, allowing more efficient re-initiation of terminating ribosomes [44]. We used the initiation rates extracted from ribosome profiling and RNA-Seq data reported in Ref. [16], and polysome profiling data reported in Ref. [42] and find a moderate but statistically significant correlation (Pearson r = 0.51, p-value = 4 × 10⁻⁵⁹) between the translation-initiation rate and the inverse of CDS length (Fig 4A), as has been observed previously [10,14,16].

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Fig 4. Translation-initiation rates measured using Eq (4) reproduce previously reported correlations with molecular properties.

In vivo translation-initiation rates of S. cerevisiae transcripts are plotted against the inverse of their CDS length, folding energy of mRNA molecule near the 5′ cap and protein copy number in (A), (B) and (C), respectively. (D) The copy number of S. cerevisiae proteins are plotted as a function of the product of the initiation rate of the transcripts that encode them and that transcript’s copy number in a cell. (E) mRNA copy number is plotted against the translation-initiation rate.

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Folded mRNA structure near the 5′ cap can disrupt the binding of initiation factor eIF4F and the scanning of 40S ribosomes in eukaryotes, causing a decrease in a gene’s translation-initiation rate [14,16,45,46]. We calculated the mRNA folding energy near the 5′ mRNA cap (see Methods) and find a statistically significant correlation between them and our translation-initiation rates (Fig 4B, Pearson r = 0.30 and p-value = 2 × 10⁻⁹).

Sequence-based features also determine the rate of translation-initiation in eukaryotes. For example, an upstream open reading frame can potentially interfere with translation initiation at the canonical start codon by initiating translation prematurely resulting in a different protein product [47,48]. We tested whether upstream open reading frames affect initiation rates by comparing the median initiation rate in transcripts with at least one upstream AUG site against transcripts that do not contain any upstream AUG. We find that the transcripts with at least one upstream AUG codon have a median initiation rate that is 15% slower (0.095 s⁻¹ versus 0.112 s⁻¹, Mann-Whitney U test, p-value = 0.006). Weinberg et al. [16] also demonstrated this effect with their measure of initiation efficiency. Additionally, the 12-nt Kozak sequence [49] is enriched in highly expressed genes and mutations in the Kozak sequence have been shown to drastically effect protein abundance levels [50]. We find that initiation rates are 16% faster with a median value of 0.116 s⁻¹ in transcripts with Kozak-like sequences around the start codon as compared to those that do not contain these mRNA sequence motifs (Mann-Whitney U test, p-value = 0.005). Hence, the presence of Kozak or Kozak-like sequences around the start codon facilitate translation initiation. This is consistent with results of Pop et al. [13] who have shown a strong correlation between the presence of the Kozak sequence and translation efficiency.

Initiation is typically the rate limiting step of translation [21]. Therefore, a faster initiation rate should increase the rate of protein synthesis and thus the steady-state level of proteins in a cell. Indeed, we find a statistically significant correlation between the rate of translation-initiation and protein copy number in a cell (Fig 4C, Pearson r = 0.29 and p-value = 1 × 10⁻⁵). Next, we tested whether the missing variation in Fig 4C is explained by the variation in mRNA copy number. We did this by measuring the correlation between the protein copy number and the multiplicative product of a transcript’s copy number and its initiation rate. We find a stronger correlation between this quantity and protein copy number (Fig 4D, Pearson r = 0.70 and p-value = 5 × 10⁻³³). These results suggest, as has been found previously [21,51], that the translation-initiation rate is a major determinant of protein abundance inside a cell.

We further measured the correlation between the mRNA copy number and initiation rates and found a moderate level of correlation between them (Fig 4E, Pearson r = 0.35 and p-value = 1 × 10⁻⁷). This suggests that higher copy number transcripts have a faster translation-initiation rate, consistent with previous studies [52]. We also find statistically significant correlations between the aforementioned quantities when we calculated the translation-initiation rate from other published data, using all possible combinations of ribosome profiling, RNA-Seq [16,43] and polysome profiling datasets [29,42] (S5–S7 Figs, S1 and S2 Tables).

In summary, we find that the initiation rates we measured correlate with factors that have been established to influence translation speed. This suggests our initiation rates are reasonable.

Measurement of the average codon translation rate in a cell.

Next, we applied Eq (7) to measure the average codon translation rate inside mouse stem cells from ribosome run-off experiments [26]. We calculated the average normalized reads from three different samples prepared by allowing the ribosomes to continue their elongation for 90, 120, and 150 seconds after the inhibition of initiation, and plotted as a function of codon position (Fig 2C). By following the analysis procedure described in the Theory Section, we fitted against Δt curves (S1B Fig) with a line and calculated the depletion time τ(L), where equals zero for L varying between codon positions 800 and 1000. Plotting τ(L) against L yields a straight line (Fig 2D). The gradient of this line is the average elongation rate, which we find equals 5.2 AA/s.

Measurement of individual codon translation rates.

To extract individual codon translation times along a coding sequence we applied Eq (12) to 117 and 364 high-coverage transcripts from ribosome profiling data reported, respectively, in Refs. [43] and [53] (see Methods). The number of transcripts in both of these datasets are small as compared to the size of S. cerevisiae transcriptome. Therefore, to determine whether these subset of transcripts are representative of the whole transcriptome we compared the distributions of different physicochemical properties in these two sets to the total transcriptome. We find that the subset of transcripts from Nissley et al. [43] have 6.6% higher mean GC content but a very similar mode of length distribution and codon usage relative to the total transcriptome (S8A–S8C Fig). For Williams et al.’s ribosome profiling dataset [53] we again find that the mode of the length distribution and codon usage is similar to the S. cerevisiae transcriptome, with 5.3% higher mean GC content (S8D–S8F Fig). This indicates that the set of transcripts we analyze are largely representative of the properties of the transcriptome, but have a bit higher GC content.

Upon extracting individual codon translation times from these ribosome profiling data, we first characterized the distribution of translation times for the 61 sense codons (S1 File). We find around three-fold difference between the median translation times of the fastest and slowest codons in the Nissley dataset [43]. The fastest and slowest codons are AUU and CCG codons that are translated in 127±2 and 344±37 ms (median ± standard error), respectively. The variability in translation times for a given codon type is even larger, as illustrated by wide distributions of their translation times in the Nissley dataset (Fig 5A, S9A Fig). Fig 5B shows an example where the AAG codon is translated with translation times ranging from 59 ms at codon position 413 to 363 ms at codon position 196 in YAL038W S. cerevisiae transcript. We find a 16-fold variability in codon translation times across the transcriptome even if we ignore the extremities of the distributions by only considering the translation times between the 5^th and 95^th percentiles of all codon types. Similar ranges are found in the Williams dataset where there is a 26-fold variability in translation times and 3.9 fold-difference in median translation times of the fastest (AUC) and slowest (CGA) codons, which are translated with median time of 128±2 and 496±61 ms, respectively (S1 File, S9B Fig). The translation time distributions are well correlated between the above two datasets (S10A and S10B Fig). The study of Dao Duc and Song [14] also infers the individual codon translation rates and a very high correlation is observed between the rates obtained using our method and the rates found in that study (S10C Fig).

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Fig 5. Wide variability in individual codon translation rates in vivo.

(A) Probability density functions for translation times of AUU, GAC and UGG codons in Nissley dataset. Median translation times for AUU, GAC and UGG codon are 127, 208 and 331 ms, respectively. (B) The translation time profile of S. cerevisiae transcript YAL038W from Nissley dataset is shown between codon positions 150 and 450. AAG codon (colored red) is translated in 362.8 ms at the 196^th codon position and in 58.6 ms at 413^th codon position.

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Molecular factors flanking the A-site shape the variability of individual codon translation rates.

A number of molecular factors have been shown or suggested to influence the translation rate of a codon in the A-site, including tRNA concentration, mRNA structure, wobble-base pairing, and proline residues at or near the ribosome P-site [16,18–20,22–24,39]. Here, we test whether the presence or absence of these factors correlate with changes in translation speed that we measure. We first examined whether the cognate tRNA concentration correlates with our translation times. We find that the median codon translation times negatively correlates with the abundance of cognate tRNA (Fig 6A and 6B, ρ = −0.51 (p-value = 0.0006) and ρ = −0.50 (p-value = 0.0009), respectively), indicating that codons with lower cognate tRNA concentrations typically are translated more slowly.

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Fig 6. Molecular factors shaping the variability of individual codon translation rates.

(A-B) Median translation times of codon types are negatively correlated with cognate tRNA abundance estimated by (A) gene copy number and (B) RNA-Seq gene expression. (C) Probability distribution of translation times of codons in the A-site either when a proline is present in the P-site (green) or when a proline is not present in the P-site (blue). (D-E) Percentage difference in median translation times when mRNA structure is present relative to when it is not present is plotted as a function of codon position after the A-site. Grey bars indicate results that are not statistically significant. Error bars are the 95% C.I. calculated using 10⁴ bootstrap cycles; significance is assessed using the Mann-Whitney U test corrected with the Benjamini Hochberg FDR method for multiple-hypothesis correction. mRNA structure information used in (D) and (E) are provided by in vivo DMS and in vitro PARS data, respectively. (F) Scatter plot of the median translation times of pairs of codon types that are decoded by the same tRNA molecule. The red line is the identity line. The list of tRNA molecule names and decoded codon types were taken from Ref. [54]. Error bars are standard error about the median translation time calculated with 10⁴ bootstrap cycles.

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The presence of a proline amino acid at the ribosome’s P-site can slowdown translation due to its stereochemistry [55]. We tested whether such an effect was present in our data set by calculating the percentage difference in median translation time at the A-site when proline is present at the P-site versus when it is not present at the P-site. We find a 19% increase in median translation time when proline is present (Fig 6C, Mann-Whitney U test, p-value = 2.2 × 10⁻³²) indicating that proline does systematically slowdown translation in vivo.

It has been found that the presence of downstream mRNA secondary structure can slow down the translation at the A-site [23,24,56,57]. To test for this effect, we plotted the difference in the median translation time at the A-site when mRNA secondary structure is present versus when it is not present at a given number of codon positions downstream of the ribosome A-site. Structured versus unstructured nucleotides were identified using DMS data [58]. We find that when secondary structure is present 4 codons downstream of the A-site, placing that structure directly at the leading edge of the ribosome, there is on average a 6.7% increase in codon translation time at the A-site (Fig 6D, Mann-Whitney U test, p-value = 2.7 × 10⁻¹⁴). A slowdown is also found when we cross-reference our codon translation times with mRNA structure data from PARS [59], which measures the presence of mRNA structure in vitro (Fig 6E, Mann-Whitney U test, p-value = 5.6 × 10⁻⁹).

Wobble base pairing between the codon and anti-codon tRNA stem-loop has been found to slowdown translation speed as compared to Watson-Crick base pairing in bacteria [60] and metazoans [61]. For each pair of codon types that are decoded by the same tRNA molecule, by Watson-Crick base pairing in one instance and wobble base pairing in the other, we tested whether two codon types are translated with different rates. We find that there is no systematic difference in median translation times between codons that are decoded by either mechanism (Fig 6F, Wilcoxon signed-rank test, p-value = 0.46), indicating that, at least in S. cerevisiae, wobble base pairing does not slowdown in vivo translation elongation.

These results were reproduced using another dataset [53] that also shows that codon translation times anti-correlate with tRNA concentration (S11A and S11B Fig, ρ = −0.58 (p-value = 7.8 × 10⁻⁵) and ρ = −0.56 (p-value = 0.0002), respectively), exhibit larger translation times when a proline is present at the P-site (S11C Fig, Mann-Whitney U test, p-value = 3.0 × 10⁻²⁷) or when mRNA structure is present downstream of the A-site (S11D and S11E Fig, Mann-Whitney U test, p-values = 3.6 × 10⁻⁵, 8.7 × 10⁻⁴, respectively) and similarly, we found no difference between the translation rate of codons that are translated with Watson-Crick and Wobble base pairing (S11F Fig, Wilcoxon signed-rank test, p-value = 0.88).

Datasets.

To calculate the translation-initiation rates we applied our methods (Eq (4)) to in vivo ribosome profiling data published in Refs. [16] and [43] with NCBI accession numbers GSM1289257 and GSM1949551, respectively. The RNA-Seq data we used for Ref. [16] has NCBI accession number GSM1969535. For Ref. [43], we make public the RNA-Seq sample at GSM3242263 which we performed simultaneously with the ribosome profiling experiment. We chose these two data sets because they contain both ribosome profiling and RNA-Seq data of a sample, allowing us to calculate the average ribosome density of a transcript (S1 Text, Eq. (S9)). To calculate the codon translation rates, we apply our method to high-coverage ribosome profiling datasets of wild type S. cerevisiae reported in Refs. [43] and [53] with NCBI accession numbers GSM1949551 and GSM1495503, respectively. In our analysis, reads were preprocessed and mapped to sacCer3 reference genome as described in Ref. [43]. To maintain the accuracy of read assignment, transcripts in which multiple mapped reads constitute more than 0.1% of total reads mapping to the CDS region were not considered in the analysis. A-site positions in ribosome profiling reads were assigned according to the offset table generated using an Integer Programming algorithm which maximizes the reads between the second and stop codon of transcripts [89]. The offset table for S. cerevisiae is taken from Table 1 of ref. [89]. RPKM values were calculated for transcripts in RNA-Seq data by counting the reads whose 5′ ends were within the coding region of the transcript.

Selection of genes for translation-initiation rates.

To apply our method (Eq (4)) for extracting translation initiation rates, we restrict our analysis to genes in which 95% of codon positions of a transcript have non-zero read density. 1,388 transcripts meet this criterion. This threshold reduces the statistical uncertainty in the estimation of codon position dependent ribosome density used in Eq (4).

Selection of genes for codon translation rates.

To extract individual codon translation rates, we restrict our analysis to genes that have at least 3 reads at every codon position of the transcript. We find that 117 and 364 genes meet this criterion in the data set of Nissley et al. [43] and Williams et al. [53], respectively. This stringent requirement is necessary since Eq (12) would predict codons with zero reads to be translated in zero time. Reads at the start codon and the second codon have contributions from the translation initiation process; therefore, we ignored these codon positions in our calculations of translation time distributions and correlation with molecular factors. As stated before, transcripts containing multiple mapped reads greater than 0.1% of the total reads mapped to the transcript were discarded. Genes with overlap of coding sequence regions as well as those containing introns (which is less than 6% of S. cerevisiae genome) were not considered in the analysis to avoid overlap of ribosome profiles.

Preparation of RNA-Seq sample.

200 mL of cells were grown in YPD to an OD_{600 nm} of 0.5, filtered (All-Glass Filter 90mm, Millipore), flash frozen in liquid nitrogen and lysed by mixer milling (2 min, 30 Hz, MM400, Retsch) with 600 μL of lysis buffer (20 mM Tris-HCl pH 8.0, 140 mM KCl, 6 mM MgCl2, 0.1% NP-40, 0.1 mg/ml cycloheximide, 1 mM PMSF, 2x protease inhibitors (Complete EDTA-free, Roche), 0.02 U/ml DNaseI (recombinant DNaseI, Roche), 20 mg/mL leupeptin, 20 mg/mL aprotinin, 10 mg/mL E-64, 40 mg/mL bestatin). Thawed cell lysates are cleared by centrifugation (20,000xg, 5 min, 4°C) and RNA extraction is performed as described in Ref. [90]. 10 μg of extracted RNA was depleted for rRNA using the kit RiboMinus, Yeast Module (Invitrogen) and fragmented for 30 min using the NEBNext Magnesium RNA Fragmentation Module (NEB). Deep sequencing libraries were prepared following the protocol described in Ref. [90] and sequenced on a HiSeq 2000 (Illumina).

Miscellaneous.

(a) Since experimental measurements of 〈T(i)〉s are not available for S. cerevisiae we use Eq. (S10) to estimate 〈T(i)〉 with 〈τ^A〉 = 200 ms, as reported in the literature [40,41]. (b) In vivo ribosome profiling data for the mouse stem cells were processed using the method described in the original paper [26]. (c) The measures for tRNA abundance based on gene copy number and RNA-Seq measurements were obtained from Table S2 of Ref. [16]. (d) Transcript leader (or 5′ UTR) sequences were obtained from Ref. [80] and upstream AUG were identified in these sequences for the transcripts for which we calculate the translation initiation rates. (e) For Kozak sequence analysis, 12 nt sequence was identified around the start codon starting from -6 with respect to Adenine of start codon (position +1) to +6. The consensus Kozak sequence for S. cerevisiae is (A/T)A(A/C)A(A/C)AATGTC(T/C) [49]. For the 12 nt sequence for every transcript, a similarity score is calculated based on its match with the Kozak sequence. The score ranges from 1 to 10 in the order of its increasing similarity with Kozak sequence. If all the 9 nt around the start codon are same as the Kozak sequence and the start codon (scored as 1), the score will be 9+1 = 10. If only start codon is same while all other 9 nt are different, the score is just 1. If start codon is same and only 4 nt positions are same, then the score will be 4+1 = 5. To determine the effect of Kozak sequence, two subsets of transcripts were created, the first with transcripts having context around start codon closer to Kozak sequence (score > 7) and the second subset for transcripts with context farther away from Kozak sequence (score < 5). Mann-Whitney U test was used to determine the statistical significance of the difference between the translation-initiation rate distributions of the two subsets of genes.