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.

Gradual ER calcium depletion induces a progressive and reversible UPR signaling.

The unfolded protein response (UPR) is a widespread signal transduction pathway triggered by endoplasmic reticulum (ER) stress. Because calcium (Ca2+) is a key factor in the maintenance of ER homeostasis, massive Ca2+ depletion of the ER is a potent inducer of ER stress. Although moderate changes in ER Ca2+ drive the ubiquitous Ca2+ signaling pathways, a possible incremental relationship between UPR activation and Ca2+ changes has yet to be described. Here, we determine the sensitivity and time-dependency of activation of the three ER stress sensors, inositol-requiring protein 1 alpha (IRE1α), protein kinase R-like ER kinase (PERK), and activating transcription factor 6 alpha (ATF6α) in response to controlled changes in the concentration of ER Ca2+ in human cultured cells. Combining Ca2+ imaging, fluorescence recovery after photobleaching experiments, biochemical analyses, and mathematical modeling, we uncover a nonlinear rate of activation of the IRE1α branch of UPR, as compared to the PERK and ATF6α branches that become activated gradually with time and are sensitive to more important ER Ca2+ depletions. However, the three arms are all activated within a 1 h timescale. The model predicted the deactivation of PERK and IRE1α upon refilling the ER with Ca2+. Accordingly, we showed that ER Ca2+ replenishment leads to the complete reversion of IRE1α and PERK phosphorylation in less than 15 min, thus revealing the highly plastic character of the activation of the upstream UPR sensors. In conclusion, our results reveal a dynamic and dose-sensitive Ca2+-dependent activation/deactivation cycle of UPR induction, which could tightly control cell fate upon acute and/or chronic stress.

Computational investigation of IP3 diffusion.

Inositol 1,4,5-trisphosphate (IP3) plays a key role in calcium signaling. After stimulation, it diffuses from the plasma membrane where it is produced to the endoplasmic reticulum where its receptors are localized. Based on in vitro measurements, IP3 was long thought to be a global messenger characterized by a diffusion coefficient of ~ 280 µm2s-1. However, in vivo observations revealed that this value does not match with the timing of localized Ca2+ increases induced by the confined release of a non-metabolizable IP3 analog. A theoretical analysis of these data concluded that in intact cells diffusion of IP3 is strongly hindered, leading to a 30-fold reduction of the diffusion coefficient. Here, we performed a new computational analysis of the same observations using a stochastic model of Ca2+ puffs. Our simulations concluded that the value of the effective IP3 diffusion coefficient is close to 100 µm2s-1. Such moderate reduction with respect to in vitro estimations quantitatively agrees with a buffering effect by non-fully bound inactive IP3 receptors. The model also reveals that IP3 spreading is not much affected by the endoplasmic reticulum, which represents an obstacle to the free displacement of molecules, but can be significantly increased in cells displaying elongated, 1-dimensional like geometries.

T cell Ca2+ microdomains through the lens of computational modeling.

Cellular Ca2+ signaling is highly organized in time and space. Locally restricted and short-lived regions of Ca2+ increase, called Ca2+ microdomains, constitute building blocks that are differentially arranged to create cellular Ca2+ signatures controlling physiological responses. Here, we focus on Ca2+ microdomains occurring in restricted cytosolic spaces between the plasma membrane and the endoplasmic reticulum, called endoplasmic reticulum-plasma membrane junctions. In T cells, these microdomains have been finely characterized. Enough quantitative data are thus available to develop detailed computational models of junctional Ca2+ dynamics. Simulations are able to predict the characteristics of Ca2+ increases at the level of single channels and in junctions of different spatial configurations, in response to various signaling molecules. Thanks to the synergy between experimental observations and computational modeling, a unified description of the molecular mechanisms that create Ca2+ microdomains in the first seconds of T cell stimulation is emerging.