Protein Synthesis Times Scale with Gene Length because the Determinants of Translation Speed are Randomly Distributed Across Genes

Abstract

Many of the molecular factors influencing codon translation speed have been identified, and their relative contributions estimated. These factors include tRNA concentration, the presence of charged nascent-chain residues in the ribosome exit tunnel, mRNA secondary structure, proline residues at the A or P sites of the ribosome and steric interactions between ribosomes translating a transcript. Here, we combine this information with genomic information from E. coli, yeast and humans in a simulation model of translation to estimate the synthesis time of cytopolasmic proteins. We find that regardless of the organism, the synthesis time of a protein scales linearly with the length of mRNA's coding sequence even though there is a large variation in the translation speed of individual codons. We demonstrate that this scaling arises because the molecular determinants of translation speed are distributed randomly across the mRNA transcripts and that this distribution is generated from a Poisson point process. As a consequence, the Law of Large Numbers is followed and for any given transcript fast-translating segments are canceled out by a similar number of slow-translating segments resulting a constant average codon translation rate between different transcripts. This means that a protein's average synthesis time can be accurately predicted based solely on the corresponding gene length, provided the average codon translation speed is known. Thus, although evolution has biased codon usage between different genes in an organism, there is still a large degree of randomness associated with how individual codon translation speeds have been distributed. These results also provide an explanation for the observation from ribosome profiling that different transcripts have the same average codon translation speed in mouse-stem cells.