Theoretical analysis of the distribution of isolated particles in the TASEP: Application to mRNA translation rate estimation

Abstract

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 translation. Applying this model to quantify translation dynamics from ribosome profiling data is not straightforward, however, and it requires characterizing the extent of interference, since the experimental protocol may be biased against nearby ribosomes. To evaluate and correct for this potential bias, we provide here a theoretical analysis of the distribution of isolated particles in the TASEP. In the classical form of the model in which each particle occupies only a single site, we obtain exact analytic solutions using the Matrix Ansatz. We then employ a refined mean field approach to extend the analysis to a generalized TASEP with particles of an arbitrary size. Our theoretical study has direct applications in mRNA translation and the interpretation of experimental ribosome profiling data. In particular, our analysis of data from S. cerevisiae suggests a potential bias against the detection of nearby ribosomes with gap distance less than ∼ 3 codons, which leads to some ambiguity in estimating the initiation rate and protein production flux for a substantial fraction of genes. Despite such ambiguity, however, we demonstrate theoretically that the interference rate can be robustly estimated, and show that approximately 1% of the translating ribosomes get obstructed. Lastly, we find that, on average, the termination rate is near optimal in that it is close to the minimum value needed to not limit the ribosome flux.

The impact of ribosomal interference, codon usage, and exit tunnel interactions on translation elongation rate variation

“…However, for this dataset, we still observe a decrease of the fitting constant for genes with higher density (0.58). In another study [46], we investigated different gap sizes using a refined analysis of the TASEP to study the relation between the total density and the density of isolated ribosomes for a specific isolation distance. The best match was obtained for a distance of 2 or 3 codons, in agreement with the model used here.…”

Performance Analysis of Ad-Hoc Networks using Statistic Mechanics

“…The TASEP link between statistical mechanics and wireless networking. this work showcases the characterizing performance parameters of a linear multi-hop traffic flow [1] [2] [3].…”