Malfunctions in the folding state of critical proteins have been linked with cancer, diabetes and other diseases. Proteins requiring complex post-translational modification are processed in the Endoplasmic Reticulum (ER). Cells monitor protein folding by an inbuilt quality-control system involving both the ER and the Golgi apparatus. Incorrectly folded proteins are tagged for degradation or sent back through a refolding cycle. However, accumulation of incorrectly folded proteins can also trigger a cascade of events, termed the Unfolded Protein Response (UPR). In this study, we developed a mathematical model of UPR, which was composed of a system of ordinary differential equations. The model was assembled as a series of molecular modules integrated together to form the UPR network. Kinetic parameters for the model were estimated by comparing simulations with a family of training constraints. Eight sets of western blot experiments were used as the training constraints. Using a multi-objective thermal annealing scheme, we generated an ensemble of models consistent with the western blot constraints. Model output was compared to eleven sets of western blot studies to test the correctness of the model. Sensitivity analysis revealed that two particular modules, the UPR initiation and apoptosis modules, were the most sensitive structural elements of the model. Coupling analysis further highlighted the importance of key nodes e.g., the release of BiP (GRP78) from the ER stress transducers or the activation of Activating Transcription Factor 4 (ATF4). Taken together, we demonstrated that modeling could be used to understand key structural elements of UPR, despite model uncertainty. Understanding the architecture of this stress pathway could help us understand the design principles governing other stress related networks, e.g., hypoxia. Thus, while the current study was limited to UPR, the general strategy could be extended to other stress networks relevant to human health.
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