A journey in UPR modelling

Protein folding and protein maturation largely occur in the controlled environment of the Endoplasmic Reticulum (ER). Perturbation to the correct functioning of this organelle leads to altered proteostasis and accumulation of misfolded proteins in the ER lumen. This condition is commonly known as ER stress and is appearing as an important contributor in the pathogenesis of several human diseases. Monitoring of the quality control processes is mediated by the Unfolded Protein Response (UPR). This response consists in a complex network of signalling pathways that aim to restore protein folding and ER homeostasis. Conditions in which UPR is not able to overcome ER stress lead to a switch of the UPR signalling program from an adaptive to a pro-apoptotic one, revealing a key role of UPR in modulating cell fate decisions. Because of its high complexity and its involvement in the regulation of different cellular outcomes, UPR has been the centre of the development of computational models, which tried to better dissect the role of UPR or of its specific components in several contexts. In this review, we go through the existing mathematical models of UPR. We emphasize how their study contributed to an improved characterization of the role of this intricate response in the modulation of cellular functions.