  Translation of mRNA into protein is a fundamental yet complex biological
process with multiple factors that can potentially affect its efficiency. Here,
we study a stochastic model describing the traffic flow of ribosomes along the
mRNA (namely, the inhomogeneous $\ell$-TASEP), and identify the key parameters
that govern the overall rate of protein synthesis, sensitivity to initiation
rate changes, and efficiency of ribosome usage. By analyzing a continuum limit
of the model, we obtain closed-form expressions for stationary currents and
ribosomal densities, which agree well with Monte Carlo simulations.
Furthermore, we completely characterize the phase transitions in the system,
and by applying our theoretical results, we formulate design principles that
detail how to tune the key parameters we identified to optimize translation
efficiency. Using ribosome profiling data from S. cerevisiae, we shows that its
translation system is generally consistent with these principles. Our
theoretical results have implications for evolutionary biology, as well as
synthetic biology.
