A data-entrained computational model for testing the regulatory logic of the vertebrate unfolded protein response.

The vertebrate unfolded protein response (UPR) is characterized by multiple interacting nodes among its three pathways, yet the logic underlying this regulatory complexity is unclear. To begin to address this issue, we created a computational model of the vertebrate UPR that was entrained upon and then validated against experimental data. As part of this validation, the model successfully predicted the phenotypes of cells with lesions in UPR signaling, including a surprising and previously unreported differential role for the eIF2α phosphatase GADD34 in exacerbating severe stress but ameliorating mild stress. We then used the model to test the functional importance of a feedforward circuit within the PERK/CHOP axis and of cross-regulatory control of BiP and CHOP expression. We found that the wiring structure of the UPR appears to balance the ability of the response to remain sensitive to endoplasmic reticulum stress and to be deactivated rapidly by improved protein-folding conditions. This model should serve as a valuable resource for further exploring the regulatory logic of the UPR.

The schedule effect: can recurrent peak infections be reduced without vaccines, quarantines or school closings?

Using a basic, two transmission level seasonal SIR model, we introduce mathematical evidence for the schedule effect which asserts that major recurring peak infections can be significantly reduced by modification of the traditional school calendar. The schedule effect is observed first in simulated time histories of the infectious population. Schedules with higher average transmission rate may exhibit reduced peak infections. Splitting vacations changes the period of the oscillating transmission function and can confine limit cycles in the proportion susceptible/proportion infected phase plane. Numerical analysis of the phase plane shows the relationship between the transmission period and the maximum recurring infection peaks and period of the response. For certain transmission periods, this response may exhibit period-doubling and chaos, leading to increased peaks. Non-monotonic infectious response is also observed in conjunction with changing birth rate. We discuss how to take these effects into consideration to design an optimum school schedule with particular reference to a hypothetical developing world context.

Regulation of the transcriptome by ER stress: non-canonical mechanisms and physiological consequences.

The mammalian unfolded protein response (UPR) is propagated by three ER-resident transmembrane proteins, each of which initiates a signaling cascade that ultimately culminates in production of a transcriptional activator. The UPR was originally characterized as a pathway for upregulating ER chaperones, and a comprehensive body of subsequent work has shown that protein synthesis, folding, oxidation, trafficking, and degradation are all transcriptionally enhanced by the UPR. However, the global reach of the UPR extends to genes involved in diverse physiological processes having seemingly little to do with ER protein folding, and this includes a substantial number of mRNAs that are suppressed by stress rather than stimulated. Through multiple non-canonical mechanisms emanating from each of the UPR pathways, the cell dynamically regulates transcription and mRNA degradation. Here we highlight these mechanisms and their increasingly appreciated impact on physiological processes.

Small-scale modeling approach and circuit wiring of the unfolded protein response in mammalian cells.

The accumulation of unfolded proteins in the endoplasmic reticulum (ER) activates a mechanism whose primary functions are to sense any perturbation in the protein-folding capacity of the cell, and correct the situation to restore homeostasis. This cellular mechanism is called the unfolded protein response (UPR). We propose a biologically plausible computational model for the UPR under ER stress in mammalian cells. The model accounts for the signaling pathways of PERK, ATF6, and IRE1 and has the advantage of simulating the dynamical (timecourse) changes in the relative concentrations of proteins without any a priori steady-state assumption. Several types of ER stress can be assumed as input, including long-term (eventually periodic) stress. Moreover, the model allows for outcomes ranging from cell survival to cell apoptosis.