The fitness landscapes of translation*

All living cells synthesize proteins by transcribing the hereditary information in their DNA into strands of messenger RNA which are subsequently translated into amino acid sequences. The genetic code that assigns triplets of nucleotides (codons) to their corresponding amino acids is redundant, since most amino acids are encoded by several codons. Mutations that change the DNA sequence (and hence the sequence of codons) but leave the amino acid sequence unchanged are called synonymous. Motivated by recent experiments on an antibiotic resistance gene, in this work we investigate genetic interactions between synonymous mutations in the framework of exclusion models of translation. We show that the range of possible interactions is markedly different depending on whether translation efficiency is assumed to be proportional to ribosome current or ribosome speed. In the first case every mutational effect has a definite sign that is independent of genetic background, whereas in the second case the effect-sign can vary depending on the presence of other mutations. The latter result is demonstrated using configurations of multiple translational bottlenecks induced by slow codons.