Determinants of translation speed are randomly distributed across transcripts resulting in a universal scaling of protein synthesis times

Ribosome profiling experiments have found greater than 100-fold variation in ribosome density along mRNA transcripts, indicating that individual codon elongation rates can vary to a similar degree. This wide range of elongation times, coupled with differences in codon usage between transcripts, suggests that the average codon translation-rate per gene can vary widely. Yet, ribosome run-off experiments have found that the average codon translation rate for different groups of transcripts in mouse stem cells is constant at 5.6 AA/s. How these seemingly contradictory results can be reconciled is the focus of this study. Here, we combine knowledge of the molecular factors shown to influence translation speed with genomic information from Escherichia coli, Saccharomyces cerevisiae and Homo sapiens to simulate the synthesis of cytosolic proteins in these organisms. The model recapitulates a near constant average translation rate, which we demonstrate arises because the molecular determinants of translation speed are distributed nearly randomly amongst most of the transcripts. Consequently, codon translation rates are also randomly distributed and fast-translating segments of a transcript are likely to be offset by equally probable slow-translating segments, resulting in similar average elongation rates for most transcripts. We also show that the codon usage bias does not significantly affect the near random distribution of codon translation rates because only about $10\%$ of the total transcripts in an organism have high codon usage bias while the rest have little to no bias. Analysis of Ribo-Seq data and an in vivo fluorescent assay supports these conclusions.

Figure 1

Illustration of the $\mathfrak{l}$-TASEP model and its parameterization. A ribosome initiates translation with rate $\alpha$ when the first five codon positions after the start codon are not blocked by another ribosome. The ribosome translates the $j\mathrm{th}$ codon position with rate $\omega \left(j\right)$ when no downstream ribosome occupies the $\left(j+10\right)\mathrm{th}$ codon position and terminates the translation process with rate $\beta$. tRNA abundance, mRNA structure, proline residues at ribosome A and P site and positively charged residues affect the translation rate of a codon and are accounted for in the model. Ribosomes in green and light-red color are translating optimal and nonoptimal codons, respectively, whereas the ribosome colored in dark-red is sterically blocked by a downstream ribosome.

Figure 2

Synthesis time of proteins scale linearly with coding sequence length. Average synthesis times of proteins as a function of the length of the corresponding coding sequence are plotted, respectively, for E. coli, S. cerevisiae, and H. sapiens in (a), (b), and (c). The cumulative probability distribution of the percent error in the predicted synthesis times is plotted in (d), (e), and (f) for E. coli, S. cerevisiae, and H. sapiens, respectively.

Figure 3

Average translation time of a gene follows the law of large numbers. The average codon translation time of a transcript versus gene length for E. coli, S. cerevisiae, and H. sapiens in (a), (b), and (c), respectively. Results are from Monte Carlo simulations of the translation process. The dotted lines represent the transcriptome-wide average codon translation time in these organisms.

Figure 4

The molecular determinants of codon translation speeds scale linearly with coding sequence length in E. coli. The number of codon positions that encode positively charged residues, proline residues, and those codon positions that take part in mRNA structure are plotted against the coding sequence length in (a), (b), and (c), respectively. The occurrence of codon positions in a transcript that pair with a tRNA whose anti-codon is UUU and carries a lysine amino acid is plotted against the transcript length (d). A histogram of the correlation coefficient $R^2$ between the transcript length and the number of codon positions in a transcript that pair with 46 unique tRNA molecules in E. coli are plotted in (e).

Figure 5

Comparison between the distribution of normalized codon translation rates in an individual gene with the global distribution of codon translation rates. (a) The distribution of codon translation rates in the E. coli gene rplO and global distribution of codon translation rates in E. coli are plotted in black data points and red bars, respectively. (b) same as (a) except for gene MRPL25 in S. cerevisiae.