The key parameters that govern translation efficiency

Abstract

Translation of mRNA into protein is a fundamental yet complex biological process with multiple factors that can potentially affect its efficiency. In particular, different genes can have quite different initiation rates, while site-specific elongation rates can vary substantially along a given transcript. Here, we analyze a stochastic model of translation dynamics to identify the key parameters that govern the overall rate of protein synthesis and the efficiency of ribosome usage. The mathematical model we study is an interacting particle system that generalizes the Totally Asymmetric Simple Exclusion Process (TASEP), where particles correspond to ribosomes. While the TASEP and its variants have been studied for the past several decades through simulations and mean field approximations, a general analytic solution has remained challenging to obtain. By analyzing the so-called hydrodynamic limit, we here obtain exact closed-form expressions for stationary currents and particle densities that agree well with Monte Carlo simulations. In addition, we provide a complete characterization of phase transitions in the system. Surprisingly, phase boundaries depend on only four parameters: the particle size, and the first, last and minimum particle jump rates. Relating these theoretical results to translation, we formulate four design principles that detail how to tune these parameters to optimize translation efficiency in terms of protein production rate and resource usage. We then analyze ribosome profiling data of S. cerevisiae and demonstrate that its translation system is generally efficient, consistent with the design principles we found. We discuss implications of our findings on evolutionary constraints and codon usage bias.

Inferring efficiency of translation initiation and elongation from ribosome profiling

“…This result is consistent with a recent study in which replacing the first 8 codons with their slower synonymous variants significantly reduced protein expression without affecting mRNA levels 45 . Furthermore, the first codons have been recognised as critical in determining protein synthesis both theoretically 12,13,47 and experimentally 46,[48][49][50] . Beyond the first 10 codons, the metagene profile of TEE further reveals a small but noticeable drop between codons 10 and 20, followed by a slow increase between codons 20 and 100.…”

“…The RPKM is proportional to the ribosome density, which in turn is assumed to be proportional to the rate of translation -the more ribosomes on a transcript, the more efficient is protein synthesis. However, a large body of work based on mathematical modelling of ribosome dynamics suggests that the protein synthesis rate is negatively affected by increased ribosome density due to ribosome collisions [11][12][13] . To which extent ribosome collisions can be found using ribosome profiling has been an active topic of research [14][15][16][17][18] One of the goals of ribosome profiling is to understand how the elongation rate along the transcript depends on the choice of codons.…”

Cytoplasmic mRNA decay factors modulate RNA polymerase II processivity in 5’ and 3’ gene regions in yeast

“…Alternatively, the trademark buildup of Pol II near TSS may simply be the result of unbalanced initiation and 5’ elongation rates. To investigate the plausibility of the latter scenario, we employed a recently developed mathematical model which considers particles moving along a 1-dimensional path that was recently applied to ribosomes (Erdmann-Pham et al 2018). We first used our computed metagene profiles to estimate reference initiation and site-specific elongation rates and then examined the results of perturbing these parameters.…”

“…Our mathematical analysis of initiation and elongation rates is based on the recently obtained analytical solutions (Erdmann-Pham et al 2018) to the Totally Asymmetric Simple Exclusion Process (TASEP). Denoting the NET-seq Pol II metagene for a given sample at position x as ρ ( x ), site-specific elongation rates λ ( x ) were approximated as λ ( x ) ≈ 1 / ( ρ ( x )(1 − ρ ( x ))) after appropriate re-scaling of ρ ( x ) to lie in the interval (0, 1).…”

“…Furthermore, deletion of XRN 1 affected Pol II elongation efficiency in a manner consistent with enhanced Pol II backtracking. We additionally employed a recently developed mathematical model (Erdmann-Pham et al 2018) to infer changes in spatial transcriptional dynamics. This methodologically novel model uses our metagene profiles to estimate baseline values for relative initiation and elongation rates while offering a framework to systematically vary unknown parameters.…”