ABSTRACT:
Erguler2013 - Unfolded protein stress response
The model investigates the mechanism by which UPR (unfolded protein response) outcome switches between survival and death.
This model is described in the article:
A mathematical model of the unfolded protein stress response reveals the decision mechanism for recovery, adaptation and apoptosis.
Erguler K, Pieri M, Deltas C.
BMC Syst Biol. 2013 Feb 21;7(1):16.
Abstract:
BACKGROUND: The unfolded protein response (UPR) is a major signalling cascade acting in the quality control ofprotein folding in the endoplasmic reticulum (ER). The cascade is known to play an accessory rolein a range of genetic and environmental disorders including neurodegenerative and cardiovasculardiseases, diabetes and kidney diseases. The three major receptors of the ER stress involved withthe UPR, i.e. IRE1a, PERK and ATF6, signal through a complex web of pathways to convey anappropriate response. The emerging behaviour ranges from adaptive to maladaptive depending on theseverity of unfolded protein accumulation in the ER; however, the decision mechanism for the switchand its timing have so far been poorly understood.
RESULTS:
Here, we propose a mechanism by which the UPR outcome switches between survival and death.We compose a mathematical model integrating the three signalling branches, and perform a comprehensivebifurcation analysis to investigate possible responses to stimuli. The analysis reveals threedistinct states of behaviour, low, high and intermediate activity, associated with stress adaptation, tolerance,and the initiation of apoptosis. The decision to adapt or destruct can, therefore, be understoodas a dynamic process where the balance between the stress and the folding capacity of the ER playsa pivotal role in managing the delivery of the most appropriate response. The model demonstratesfor the first time that the UPR is capable of generating oscillations in translation attenuation and theapoptotic signals, and this is supplemented with a Bayesian sensitivity analysis identifying a set ofparameters controlling this behaviour.
CONCLUSIONS:
This work contributes largely to the understanding of one of the most ubiquitous signalling pathwaysinvolved in protein folding quality control in the metazoan ER. The insights gained have direct consequenceson the management of many UPR-related diseases, revealing, in addition, an extended listof candidate disease modifiers. Demonstration of stress adaptation sheds light to how preconditioningmight be beneficial in manifesting the UPR outcome to prevent untimely apoptosis, and paves the wayto novel approaches for the treatment of many UPR-related conditions.
In the paper, PERKA refers to the amount of phosphorylated PERK monomer. However, it refers to the active complex in the model. The complex with the model parameterization is formed of 4 monomers (n=4). So, the value of PERKA should be multiplied by 4, in order to generate the figures in the paper (eg. Figure 12).
An additional parameter (tmr=10)) is used in the model. This parameter is not mentioned in the paper. The model values of kf(=10) and kr(=1) are not consistent with that of the paper (kf=100, kr=10, in the paper). However, this is corrected by the introduction of "tmr" in the model, which is multiplied with kf and kr to get the resulting values.
The term "tmr" was missing in the kinetic laws of the reactions reu7 and reu8, in the original model. This has been corrected as per the author's request.
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Kamil Erguler 
