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.
