PMC

G1/S time and caspase 3 activities as a function of IRR.

Phase plane plots of CycB and Wee1 nullclines in G2/M checkpoint without (a) and with (b) exposure to IR. These plots show that larger cell mass (m) is required (0.85 vs. 0.64) for switching out of G2/M in the presence of DNA damage under exposure to IR.

Comparison of model prediction and transformed experimental data for dose response curve of caspase 3 activity versus ¹³⁷Cs-irradiated lymphoblastoid cells. Original data from (Experimental condition: dose: 5, 10 and 20 Gy).

IR-mediated DNA damage, sensing of the damage by ATM, p53-dependent G1/S and G2/M cell cycle checkpoints and apoptosis. ( and —| imply activation and repression, respectively. Note the central role of p53 in the signaling pathways. The large ovals at the bottom left and right indicate proteins and interactions in the G1/S and G2/M checkpoints, respectively.

At the highest dose evaluated (Case 4, IRR = 1, Δt = 20), caspase activity was predicted to increase the likelihood for apoptosis dramatically (, bottom panel). An increased likelihood of apoptosis in the presence of high levels of DNA damage has been seen experimentally ().

Analysis of protein activities at G1/S checkpoint for different doses of IR for CycE, Rb, DSB, caspase 3. Increasing doses of IR lead to increased levels of DSB (a–d, bottom panels), increased durations of checkpoint arrest as indicated by switching of CycE and Rb (a–d, top panels), and increased probability of apoptosis as indicated by increased levels of caspase3 (a–d, bottom panels). a) Case1: IRR = 0.01, Δt = 10; b) Case 2: IRR = 0.3, Δt = 10; c) Case 3: IRR = 0.5, Δt = 20; d) Case 4: IRR = 1, Δt = 20.

Comparison of model prediction and transformed experimental data for time course of p53p activity in carbon ion-irradiated confluent fibroblasts. Original data from ). (Simulation condition: IRR = 0.18, t = 40 unit; Experimental condition: dose: 0.5 Gy; measuring time: 0, 1.5, 3, 6, 12, 24 hours after radiation, respectively).

Comparison of model prediction and transformed experimental data time course of p21 activity in carbon ion-irradiated confluent fibroblasts. Original data from . (Simulation condition: IRR = 0.5, t = 10 unit; Experimental condition: dose: 0.5 Gy; exposure duration: 0, 1.5, 3, 6, 12, 24 hours after radiation, respectively).

Biphasic (hormetic) Dose-response Model for Cancer Incidence (the percent response in the controls must be non-zero). Protection is “optimized” because it is greatest at a dose range furthest away from a non-zero percentage response in the controls. The black dots identify exposure-response points that are – or should be – included in any complete analysis otherwise the empirical relationship (based on the white dots) cannot be estimated and thus the default appears to be sound when it is not.

Phase plane plots of CycE and Rb nullclines in G1/S checkpoint without (a) and with (b) exposure to IR. The three panels for (a) show that, as cell mass (m) increases (0.33 ‡ 0.39 ‡ 0.5), the Rb nullcline moves to the left relative to the CycE nullcline and the stable steady state at low CycE disappears, triggering the switch to S phase. Under exposure to IR, the switch is activated only at higher m, thus allowing extra time for DNA repair.

Exposure to a higher dose of IR (Case 2, IRR = 0.3, Δt = 10) was predicted to delay the switch-like transitions in the activities of CycE and Rb (, top panel), indicating arrest at the G1/S checkpoint. In this case the level of DNA damage (, bottom panel) is sufficient to activate the signal transduction pathway and alter the time-course activities of the key regulatory activities at the checkpoint, providing additional time for DNA repair. This dose of IR was predicted to cause only a small increase caspase activity (, bottom panel).

Exposure to a still higher dose of IR (Case 3, IRR = 0.5, Δt = 20) was predicted to trigger a correspondingly longer checkpoint arrest (, top panel). The duration of the checkpoint arrest was predicted to be sufficient in this case to allow caspase activity to increase to a level associated with an apparently improved possibility of entry into the apoptotic pathway (, bottom panel). With a sufficiently long checkpoint arrest, it is reasonable to think that some of the cells go into apoptosis during the arrest period; thus this prediction is consistent with data showing that cell survival is reduced in association with p53-dependent G1 arrest ().