Robust Flows over Time: Models and Complexity Results

We study dynamic network flows with uncertain input data under a robust optimization perspective. In the dynamic maximum flow problem, the goal is to maximize the flow reaching the sink within a given time horizon $T$, while flow requires a certain travel time to traverse an edge. In our setting, we account for uncertain travel times of flow. We investigate maximum flows over time under the assumption that at most $\Gamma$ travel times may be prolonged simultaneously due to delay. We develop and study a mathematical model for this problem. As the dynamic robust flow problem generalizes the static version, it is NP-hard to compute an optimal flow. However, our dynamic version is considerably more complex than the static version. We show that it is NP-hard to verify feasibility of a given candidate solution. Furthermore, we investigate temporally repeated flows and show that in contrast to the non-robust case (that is, without uncertainties) they no longer provide optimal solutions for the robust problem, but rather yield a worst case optimality gap of at least $T$. We finally show that the optimality gap is at most $O(\eta k \log T)$, where $\eta$ and $k$ are newly introduced instance characteristics and provide a matching lower bound instance with optimality gap $\Omega(\log T)$ and $\eta = k = 1$. The results obtained in this paper yield a first step towards understanding robust dynamic flow problems with uncertain travel times

Inhibition of MYC translation through targeting of the newly identified PHB-eIF4F complex as therapeutic strategy in CLL

Dysregulation of messenger RNA (mRNA) translation, including preferential translation of mRNA with complex 5′ untranslated regions such as the MYC oncogene, is recognized as an important mechanism in cancer. Here, we show that both human and murine chronic lymphocytic leukemia (CLL) cells display a high translation rate, which is inhibited by the synthetic flavagline FL3, a prohibitin (PHB)-binding drug. A multiomics analysis performed in samples from patients with CLL and cell lines treated with FL3 revealed the decreased translation of the MYC oncogene and of proteins involved in cell cycle and metabolism. Furthermore, inhibiting translation induced a proliferation arrest and a rewiring of MYC-driven metabolism. Interestingly, contrary to other models, the RAS-RAF-(PHBs)-MAPK pathway is neither impaired by FL3 nor implicated in translation regulation in CLL cells. Here, we rather show that PHBs are directly associated with the eukaryotic initiation factor (eIF)4F translation complex and are targeted by FL3. Knockdown of PHBs resembled FL3 treatment. Importantly, inhibition of translation controlled CLL development in vivo, either alone or combined with immunotherapy. Finally, high expression of translation initiation–related genes and PHBs genes correlated with poor survival and unfavorable clinical parameters in patients with CLL. Overall, we demonstrated that translation inhibition is a valuable strategy to control CLL development by blocking the translation of several oncogenic pathways including MYC. We also unraveled a new and direct role of PHBs in translation initiation, thus creating new therapeutic opportunities for patients with CLL