A Deterministic Model for Non-monotone Relationship Between Translation of Upstream and Downstream Open Reading Frames

The TASEP modeling was shown to offer a parsimonious explanation for the experimentally confirmed ability of a single upstream Open Reading Frames (uORFs) to upregulate a downstream translation during the integrated stress response. As revealed by the numerical simulations, the model predicts that reducing the density of scanning ribosomes upstream of certain uORFs increases the flow of ribosomes downstream. To gain a better insight into the mechanism which ensures the counter intuitive non-monotone relation between the upstream and the downstream flows we propose a phenomenological deterministic model to approximate the modified TASEP model of the translation process. We establish the existence of a stationary solution featuring the decreasing density along the uORF for the deterministic model. Further, we find an explicit non-monotone relation between the upstream ribosome density and the downstream flow for the stationary solution in the limit of increasing uORF length and increasingly leaky initiation. The stationary distribution of the modified TASEP model, the stationary solution of the deterministic model and the explicit limit are compared numerically.