abstract: Understanding how codon choice affects mRNA translation is one of the long-standing questions in molecular biology. Recent advances in next-generation sequencing allow us to monitor translation at a single-nucleotide resolution and mathematical modelling is now required to interpret the new data. A standard mathematical model for mRNA translation -- the totally asymmetric simple exclusion process (TASEP) -- has been known for almost fifty years, yet its steady-state solution is still unknown. I will present a power series method for solving the TASEP in the regime of small initiation rate and discuss how the solution can be used to get new insights on translational efficiency in the cell.