Density of isolated particles and the hydrodynamic limit of generalized TASEP models: Application to mRNA translation rate inference

The Totally Asymmetric Exclusion Process (TASEP) is a classical stochastic model for describing the transport of interacting particles, such as ribosomes moving along the mRNA during protein translation. As recent experimental advances (called Ribo-seq) allow to examine position-specific densities of ribosomes, analytical tools for interpreting such data are needed. We hence revisit the TASEP theory and obtain new results. Motivated by possible biases in detecting ribosomes, we first study the density of isolated particles, by using the Matrix Ansatz to obtain exact formulas and a mean-field approximation for particles with arbitrary size (l-TASEP), both of which agree well with simulations. Second, we consider the hydrodynamic limit of the l-TASEP with heterogeneous rates. We derive and analyze the associated PDE, and obtain a phase diagram that generalizes previous results obtained on simpler models. Finally, we directly apply our theoretical study to Ribo-seq data. We infer the collision rate and the gap distance of nearby ribosomes leading to non-detection, and show that although the average number of ribosome per mRNA is widely used as a proxy for the flux, it actually leads to identification ambiguity for a substantial fraction of genes.