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Erguler et al., (2013). A mathematical model of the unfolded protein stress response reveals the decision mechanism for recovery, adaptation and apoptosis.

November 2014, model of the month by Vijayalakshmi Chelliah
Original model: BIOMD0000000446


Numerous environmental, physiological and pathological insults, as well as nutrient fluctuations, disrupt the protein-folding environment of the endoplasmic reticulum (ER). As a consequence, unfolded and misfolded proteins get accumulated in the ER, which is referred to as ER stress. The ER respond to ease the stress caused due to the accumulation of unfolded proteins by activating specific intracellular signalling pathways, which is collectively termed as the unfolded protein response (UPR).

Glucose deprivation, disruption of calcium homeostasis and ageing are known to induce ER stress and the UPR. The UPR activation is also involved in a range of neurological disorders such as Alzheimer’s, Parkinson’s, prion-related diseases and amyotrophic lateral sclerosis, and also in many other pathological conditions including type II diabetes, atherosclerosis and heart failure, glomerulonephritis and acute kidney injury [1]. Besides this, ER stress and UPR activation have important roles in every aspect of cancer development [2]. The emerging evidence from animal models about the involvement of the UPR in diverse diseases makes it an attractive pathway to target for drug discovery.

When there is a prolonged production of misfolded and unfolded proteins, the UPR signalling cascade gets activated. The outcome of UPR activation involves transient attenuation of protein synthesis, increased capacity for protein trafficking through the ER, protein folding and transport, and increased protein degradative pathway, including ER-associated degradation (ERAD). If these adaptive mechanism cannot resolve the protein-folding defect, cells enter apoptosis. On mammalian ER membrane there exists three well-known sensors of unmitigated unfolded protein (UFP) accumulation: IRE1α, PERK and ATF6. Each of these receptors is connected with a unique downstream pathway processing the stress signal into an appropriate response, ranging from adaptive (aiding protein folding and removing unfolded proteins) to maladaptive (apoptosis) response. The complete UPR signalling cascade is shown in Figure 1.

Although the UPR signalling pathway has been well established, the decision mechanism for switching between adaptive and maladaptive response, the differential responses of three UPR signalling branches against various stress levels and stress sources, and cross-talk between other signalling pathways are yet to be uncovered. Erguler et al. (2013) [3] have proposed a mathematical model of UPR signalling cascade and used it to explain how decisions are made to generate an appropriate response under prolonged stress conditions of various strengths. The model integrates the adaptive and maladaptive response mechanisms of the three UPR signalling pathways, their cross-talk, and the associated genetic and post-translational interactions into a coherent mechanistic model. The model incorporate highly detailed enzymatic and genetic regulatory interactions based on the literature information.

Figure 2

Figure 2The wiring diagram of the complete UPR model. The figure shows a) the four main functional modules, the receptor activation module, the (two) adaptive response modules and the translation attenuation module interconnected to each other, and b) the mitochondrial apoptosis (BH3-BCL2-BAX) model that is connected to the main UPR model assuming that CHOP blocks the expression of BCL-2 and activates the transcription of BH3. Figure 2a is taken from [3] and Figure 2b is taken from [5].

In addition, the above model is connected to an apoptotic module to investigate the effect of UPR activation on the timing of apoptosis. The condensed version of the mitochondrial BAX/BAK/BH3 apoptosis model of Zhang et al. (2009) [4] that is described in Tyson et al. (2011) [5] is connected to the main model assuming that CHOP blocks the expression of Bcl-2 and activates the transcription of Bim. Figure 2a shows the simplified diagram of the four main functional modules and Figure 2b shows the mitochondrial apoptotic model that is connected to the main model. So, the complete model includes all four functional modules as well as the apoptosis module composed into a single coherent system, and this model is available from BioModels BIOMD0000000446.

Model predictions

The major prediction of the model is the existence of three identifiable states of behaviour that the UPR might exhibit. The UPR can exhibit low activity state, intermediate activity state and high activity state depending on the level and duration of stress, and also the availability of BiP.

Low activity state (Figure 3a) is characterised by both the levels of UFP and the elevated folding capacity. At this stage, the effort is focused on the elevation of BiP, assisting protein folding and preventing further activation of the UPR. The model suggests that BiP can act both as a positive regulator and as a negative regulator of the UPR by switching between the receptors and UFP. This assigns the chaperone a pivotal role during the low activity state where it helps to coordinate the development of stress adaptation.

Adaptation is compromised when the limit of BiP synthesis is reached. In case of severe stress conditions (Figure 3c), BiP fails to cope with extreme UFP and also to suppress UPR activation. This results in the elevation of apoptotic signals and the irreversible activation of the BAX/BAK/BH3 pathway.

The model predicts an intermediate state of activity (Figure 3b) during which CHOP is activated but has yet to reach its upper limit. During this state, many system components involved in translation attenuation and apoptotic signals undergo oscillations. Oscillations occur as a result of differences in the kinetics of eIF2α phosphorylation/dephosphorylation and genetic regulation, and this plays a crucial role in resuming translation at least for brief periods of time. Translation is beneficial at this stage to continue vital cellular functions, especially in the synthesis of apoptotic genes if the apoptosis is initiated.


Developing adaptation, or preconditioning in clinical terms enables the elevation of folding capacity, and BiP, resting the system at the low activity state. When the intermediate state is reached from there, BAX remains low at the inactive branch of the bistable regime providing protection from apoptosis. The major contribution of oscillatory behaviour to the outcome of the UPR is the resuming of translational activity. Demonstration of stress adaptation provides a mechanistic explanation as to how preconditioning might prevent the initiation of apoptosis.

The majority of the parameters values used in the model have not been measured experimentally. Hence, rather than inferring a narrow range of parameter values, the behaviour of the system has been analysed with a wide range of parameter space. Nevertheless, the model predictions agree with several experimental observations (refer to the main paper [2]). The authors have mentioned in the paper that to validate the predictions of the model, they aim at designing a titration experiment where the ER is subjected to different stress conditions to observe if the three distinct types of behaviour occurs. Also, the model can be configured with mutational state to represent any UPR related diseased condition. As experimental observations accumulate, the model predictions and experimental observations will form a strong basis in understanding the complete UPR signalling mechanism.

Figure 1

Figure 1The unfolded protein response (UPR) signalling pathways. Figure taken from [2].

Model Description

The model comprises four main functional modules interconnected to each other:

  • The receptor activation module describes the dynamics of all the three membrane receptors, IRE1α, PERK and ATF6, in response to the UFP accumulation. The model assumes that the control of the receptor activation is through the competitive binding of the chaperone immunoglobulin heavy-chain binding protein (BiP) to the receptors and UFP, and also that the phosphorylated/active complex is capable of reversing to its inactive monomeric state without the need of an external phosphatase.
  • The two adaptive response modules that are associated with IRE1α and ATF6 branches, which together controls XBP1 dynamics and BiP synthesis.
    • Upon activation, each active domain of IRE1α catalyses the unconventional splicing of the XBP1 mRNA, which in turn translates into a transcription factor enhancing BiP synthesis. ATF6 branch is connected to the IRE1α branch through the regulation of XBP1 and BiP mRNA. In response to the activation of IRE1α, 3 to 4 times increase in BiP, and the splicing of a majority of XBP1 mRNA is expected.
    • Upon activation, ATF6 is released from BiP and traffics to the Golgi apparatus for processing by proteases to generate the active cytoplasmic domain which is a transcription activator that activates XBP1, BiP and CHOP. This links the adaptive response and translation attenuation (see below) modules together. The negative regulation of ATF6 by WFS1 is also introduced in the model (see figure 6 of [3]).
  • The translation attenuation module describes the control of translation and the apoptotic signals. Upon activation, PERK phosphorylates and deactivates the eukaryotic initiation factor eIF2α, which results in increased translation of ATF4. This triggers the activation of CHOP and subsequently GADD34, which negatively regulates eIF2α phosphorylation and restores translation.

Figure 3

Figure 3The low, intermediate and high activity states of the UPR. a) In the low activity site (i.e. at mild stress condition), rapid but transient activation of CHOP is followed by the recovery of translational activity. b) In the intermediate activity state (i.e. at moderate stress condition) both CHOP and the rate of translation exhibits sustained oscillations. c) In the high activity state (i.e. at severe stress condition), the elevated and sustained UPR activity is shown. In this condition, apoptotic signals (CHOP, BAX) are activated and the translation rate (eIF2α) is severely reduced. Figure taken from [3].

Bibliographic references

  1. Hetz et al. Targetting the unfolded protein response in disease. Nat Rev Drug Discov. 2013 Sep;12(9):703-19.
  2. Wang and Kaufman. The impact of the endoplasmic reticulum protein-folding environment on cancer development. Nat Rev Cancer. 2014 Sep;14(9):581-97.
  3. Erguler et al. A mathematical model of the unfolded protein stress response reveals the decision mechanism for recovery, adaptation and apoptosis. BMC Syst Biol. 2013 Feb 21;7:15.
  4. Zhang et al. Computational analysis of dynamical responses to the intrinsic pathway of programmed cell death. Biophys J. 2009 Jul 22;97(2):415-34.
  5. Tyson et al. Dynamic modelling of oestrogen signalling and cell fate in breast cancer cells. Nat Rev Cancer. 2011 Jun 16;11(7):523-32.