Fig 1.
Module 1 (M1), primary mechanism (PM), and module 2 (M2), secondary mechanism (SM) under normal conditions (NC).
A: Network of e5 and e2B binding with e2GDP along with the competition and displacement reaction in PM. Along with the competition between e5 and e2B, we introduce an additional displacement reaction in which e2B displaces e5 from e2GDP. B: Bifurcation diagram of Ce2 with total e2B (e2BT) as the parameter with different concentrations of total e5 (e5T) ranging from 0 – 100 nM. C: The response coefficient (RC) plot of Ce2 with e2BT as the parameter. D: Network of e5 and e2B binding with TC along with the competition and displacement reaction in SM. Along with the competition between e5 and e2B, e5 displaces e2B from TC. E: Bifurcation diagram of C2 with total e2B (e2BT) as the parameter with different concentrations of total e5 (e5T) ranging from 0 – 100 nM. F: The response coefficient (RC) plot of C2 with e2BT as the parameter. The RC is given by . The XPPAUT files used for simulations is in the supplementary S7 Fig1A.ode, and S8 Fig1D.ode.
Fig 2.
Module 1 (M1), primary mechanism (PM) and Module 2 (M2), secondary mechanism (SM), and Module 3 (M3) GDP-GTP exchange under normal conditions (NC).
A: Network of translation initiation under normal conditions. B: Bifurcation diagram of e2GTP with e2BT as parameter keeping e5T at 30 nM showing ultrasensitive and biphasic dynamics. C: Bifurcation diagram of TC with e2BT as parameter keeping e5T at 30 nM showing ultrasensitive and biphasic dynamics. D: Bifurcation diagram of e2GTP with total e2B (e2BT) as the parameter with different concentrations of total e5 (e5T) ranging from 30 – 500 nM. E: The response coefficient (RC) plot of e2GTP with e2BT as the parameter. The RC is given by . The RC is shown only for the ultrasensitive plots. F: Bifurcation of e2GTP with e2BT as the parameter showing bistable dynamics. With the increase in e2BT concentration, the system switches from a lower steady state to a higher steady state, corresponding to termination and initiation of translation, respectively. The total concentrations of free e2, e5, tR, GTP, and GDP were kept constant at 500, 250, 2500, 1200 and 40 nM, respectively. G: Bifurcation diagram of TC with total GTP (GTPT) as parameter keeping the ratio of
showing ultrasensitive dynamics. The RC plot in the inset shows ultrasensitivity. H: Bifurcation diagram of TC with GTPT as parameter keeping the ratio of
showing bistable dynamics. I: Bifurcation diagram of TC with GTPT as parameter keeping the ratio of
showing graded response. The inset’s RC plot shows a graded response. The XPPAUT file used for simulations is in the Supporting information S9 Fig2A.ode.
Table 1.
Network summary.
Table 2.
Kinetic parameters.
Fig 3.
Module 1 (M1), the primary mechanism (PM), and Module 2 (M2), the secondary mechanism (SM) under normal (NC) and stressful (SC) conditions along with the phosphorylation and dephosphorylation reactions (PdP).
A: Primary mechanism of translation initiation under normal and stressful conditions. This network captures all the interactions involving e5 and e2B with e2 and the phosphorylation and dephosphorylation reactions. B: Bifurcation diagram of e2pGDP with total kinase (kinT) as the parameter. The level of kinT represents the amount of stress. With the increase in kinT concentration, the concentration of e2pGDP switches from lower to higher, which indicates translation attenuation. In this context, the two bistable states correspond to translation attenuation and recovery. The total concentrations of free e2, e2B, e5, PP, and GDP were kept constant at 55, 2, 35, 3, and 1260 nM, respectively. C: Stress-destress plane, kinT and PPT, are the two parameters used to show the attenuation and recovery of translation. The region within the green line represents the bistable region. The yellow dot represents the neutral state of the checkpoint. As the arrows point in the diagram, the checkpoint is engaged towards the right of the neutral checkpoint, and on the left, the checkpoint is disengaged. The activation and deactivation correspond to translation attenuation and recovery, respectively. D: Secondary mechanism of translation initiation under normal and stressful conditions. This network captures all the interactions involving e5 and e2B with TC and the phosphorylation and dephosphorylation reactions. E: Bifurcation diagram of TCp with total kinase (kinT) as the parameter. The two bistable states correspond to translation attenuation and recovery. The total concentrations of free TC, e2B, e5, and PP were kept constant at 50, 18, 40, and 4 nM, respectively. F: Stress-destress plane, kinT and PPT, are the two parameters used to show the attenuation and recovery of translation. The XPPAUT files used for simulations is in the Supporting information S10 Fig3A.ode, and S11 Fig3D.ode.
Fig 4.
Network of integrated stress response.
This circuit gives an overview of integrated stress response in the translation process. The entire network is divided into three modules: module 1 (R1-R11): primary mechanism (M1: PM), module 2 (R15-R24): secondary mechanism (M2: SM), and module 3 (R12-R14): coupling of primary and secondary mechanism by GDP-GTP exchange (M3: GDP-GTP Exchange). The reactions in M1 and M2 are further grouped into normal conditions (NC), stressful conditions (SC) and phosphorylation-dephosphorylation reactions (PdP). The phosphorylated species are shown in yellow boxes, and the unphosphorylated species in green boxes where e2 is the short form of free eIF2, and TC is the short form of the ternary complex, which is a complex of e2GTP and Met-tRNA represented by tR shown in red box. Other species, kinase (kin), phosphatase (PP), GDP, and GTP are in red boxes. The eukaryotic initiation factors eIF5 (e5) and eIF2B (e2B) are given in grey boxes. All the reactions are based on mass action kinetic laws. The blue lines represent the phosphorylation and dephosphorylation reactions. Also, the red lines are for GDP-GTP exchange and ternary complex formation. The NET file for the circuit is given in the Supporting information S6 Fig4.NET.
Fig 5.
Effect of GTP on bistable dynamics for a constant under ISR.
A: Bifurcation diagram of e2pGDP with total kinase (kinT) as the parameter. We keep the total GTP (GTPT) at 150 nM. The inset contains the response coefficient (RC) graph. The RC graph shows a graded response. The bifurcation shows bistability. B: Bifurcation diagram of e2pGDP with kinT as the parameter. We keep GTPT at 400 nM. The inset contains the RC graph to show the presence of ultrasensitivity. The bifurcation shows bistability is followed by ultrasensitivity. C: Bifurcation diagram of e2pGDP with kinT as the parameter. We keep GTPT at 1500 nM. The bifurcation shows tristability. The first jump shown in green arrows is attributed to the translation attenuation and recovery by the primary mechanism (PM). The second jump shown in red arrows is attributed to the translation attenuation and recovery by the secondary mechanism (SM). D: Bifurcation diagram of TCp with kinT as the parameter. We keep GTPT at 150 nM. E: Bifurcation diagram of TCp with kinT as the parameter. We keep GTPT at 400 nM. F: Bifurcation diagram of TCp with kinT as the parameter. We keep GTPT at 1500 nM. The bifurcation shows tristability. We keep . The XPPAUT file used for simulations is in the Supporting information S12 Fig4.ode.
Fig 6.
Bifurcation diagram and stress-destress plane using ISR network.
Bifurcation diagram of e2pGDP with total kinase (kinT) as the parameter. The first jump, shown by the green arrows, represents translation attenuation and recovery by the PM. The second jump, shown by the red arrows, represents the translation attenuation and recovery by the SM. With the increase in kinT concentration, the concentration of e2pGDP switches from a lower to a higher state in two jumps. However, when kinT decreases with the decrease in stress, the system switches to the lowest state in one jump to start the translation process immediately. The insets show the stress-destress plane, kinT and PPT are the two parameters used to show the translation attenuation and recovery by PM and SM. The region within the green line represents the first jump corresponding to the PM. The region within the red line represents the second jump corresponding to the SM. The yellow dot represents the neutral state of the checkpoint. As the arrows point in the diagram, the checkpoint is engaged towards the right of the neutral checkpoint, and on the left, the checkpoint is disengaged. The translation attenuation and recovery happen in two stages: PM (green arrows) and SM (red arrows). The total concentrations of free e2, e2B, e5, PP, GTP, GDP, and tR were kept constant at 310, 53, 100, 24, 1500, 1510, and 310 nM, respectively. The XPPAUT file used for simulations is in the Supporting information S12 Fig4.ode.
Fig 7.
Bifurcation of e2pGDP at different ratios of .
A: Bifurcation diagram of e2pGDP using the primary mechanism (PM) alone, with total kinase (kinT). We keep . B: Bifurcation diagram of e2pGDP using PM alone with kinT as the parameter showing bistability. We keep
. The jump is attributed to the translation attenuation and recovery C: Bifurcation diagram of e2pGDP using PM alone with kinT. We keep
. D: Bifurcation diagram of e2pGDP using both PM and secondary mechanism (SM) with kinT as the parameter showing bistability. We keep
. E: Bifurcation diagram of e2pGDP with kinT as the parameter showing tristability. We keep
. The first jump shown in green arrows is attributed to the translation attenuation and recovery by the PM. The second jump shown in red arrows is attributed to the translation attenuation and recovery by the SM. F: Bifurcation diagram of e2pGDP using both PM and SM with kinT as the parameter showing bistability. We keep
. In all the figures, we keep the total GTP (GTPT) at 1500 nM. The XPPAUT files used for simulations are in the Supporting information S10 Fig3A.ode and S12 Fig4.ode.
Table 3.
ISR network: modules and their corresponding reactions.