Fig 1.
Simplified scheme of the model.
Arrow-headed dashed lines indicate positive transcriptional regulation, arrow-headed solid lines—protein transformation, circle-headed solid lines—positive influence or activation, hammer-headed solid lines—inhibitory regulation. Pro-survival and cell cycle-promoting proteins are represented with blue boxes, pro-apoptotic proteins with yellow boxes, proteins involved in cell cycle arrest with green boxes. Details of the cell cycle arrest module and the apoptotic module are shown in Figs 2 and 3 respectively.
Fig 2.
Scheme and the bifurcation diagram for the cell cycle arrest module.
(A) Scheme: cell cycle-arresting proteins are represented with green boxes, proteins promoting cell cycle with blue boxes, other proteins or complexes with gray boxes. Bold ‘P’ denotes a phosphorylated protein residue. The arrow notation is same as in Fig 1. (B) Bifurcation diagram of CycE vs. p53ARRESTER (bifurcation parameter). The stable and unstable steady states are indicated by solid and dashed lines, respectively. SN1 and SN2 denote saddle-node bifurcations. The number of eigenvalues with positive real parts is either one (1+) for the unstable steady state or zero (0+) for stable steady states.
Fig 3.
Scheme and the bifurcation diagrams for the apoptotic module.
(A) Scheme: pro-survival proteins are in blue boxes, pro-apoptotic proteins are in yellow boxes, other proteins or protein complexes are in gray boxes. The arrow notation is same as in Fig 1. (B) Saddle—node bifurcations line in the (p53KILLER, Aktp)-plane (2-D bifurcation diagram) separates the region of parameters for which apoptotic and survival states coexist from the region for which only the apoptotic state exists. (C) Bifurcation diagram for Casp vs. p53KILLER (bifurcation parameter) for Aktp; the saddle-node bifurcation point SN is (p53KILLER, Caspbif) ≅ (0.95×105, 1.5×103). (D) Bifurcation diagram for Casp vs. Aktp (bifurcation parameter) for p53KILLER ≅ 5×105; the saddle-node bifurcation point SN is (Aktp, Caspbif) ≅ (4.4×104, 1.5×103). The solid and dashed lines correspond respectively to the stable and unstable steady states. The number of eigenvalues with positive real parts is either one (1+) for the unstable steady state or zero (0+) for stable steady states. Notice the logarithmic scale on vertical axes in (C) and (D).
Fig 4.
Two-dimensional bifurcation diagram showing various types of bifurcation lines and points in the (Wip1 synthesis rate, PTEN synthesis rate)-plane.
The black dot indicates nominal values of parameters s1 and s2. The bifurcation lines divide the parameter domain into seven subdomains D1,…,D7. The recurrent solutions in each of these domains are given in main text. Bifurcation diagrams in Fig 5A and 5B show the recurrent solutions obtained for s1 = 0.2 and s1 = 0.4, as indicated by black arrows, and varied s2.
Fig 5.
Bifurcation diagram of p53KILLER vs. PTEN mRNA synthesis rate (s2).
(A) Wip1 synthesis rate s1 = 0.2, (B) s1 = 0.4. The stable and unstable steady states are indicated by solid and dashed lines, respectively. Ranges of stable and unstable limit cycles are indicated by dark and light blue lines, respectively; dots and open circles are the maxima and minima of the stable and unstable limit cycles, respectively. Green vertical line in (A) shows Neimark—Sacker bifurcation (N—S). Red dots mark saddle-node bifurcations (SN1, SN2), orange dots mark supercritical Hopf (Hsuper) and subcritical Hopf (Hsub) bifurcations. The numbers in format n+ adjacent to the steady state lines denote the number of eigenvalues with the positive real parts. Notice the logarithmic scale on vertical axes.
Fig 6.
Deterministic simulation trajectories of the system with the suppressed DNA repair and either nominal or perturbed mRNA synthesis rates in response to 2-Gy irradiation.
(A) Nominal Wip1 and PTEN mRNA synthesis rates (s1 = 0.1, s2 = 0.03). (B) Decreased PTEN mRNA synthesis rate (s2 = 0.005). (C) Decreased PTEN mRNA synthesis rate (s2 = 0.005) and zero Wip1 synthesis rate (s1 = 0). The simulation started at Time = 0 h from the steady state corresponding to the resting (unstimulated) cell. At Time = 10 h the irradiation phase started and lasted for 10 min. The faded line visualizes the trajectory after the initiation of apoptosis, and thus must be interpreted with caution.
Fig 7.
Deterministic simulation trajectories of the intact system in response to 2-Gy and 10-Gy irradiation.
(A) 2-Gy irradiation is insufficient to trigger apoptosis and after several oscillations system recovers to the survival steady state. (B) 10-Gy irradiation is sufficient to trigger apoptosis: after two oscillations p53KILLER stabilizes at a high level triggering apoptosis.
Fig 8.
Critical irradiation doses as a function of Wip1 (s1) and PTEN (s2) mRNA synthesis rates.
(A) Active PI3K level is decreased 2-fold from the nominal value. (B) The nominal value of active PI3K. (C) Active PI3K level is twice the nominal value. Color lines show the critical irradiation doses in the (s1, s2)-parameter space. Dashed line corresponds to the persistent (irreparable) DNA damage equal 100 DSBs. For each dose, the line separates the apoptotic region (above the line) and the survival region (below the line) in the (s1, s2)-parameter space. The black dot in (B) corresponds to nominal values of Wip1 and PTEN mRNA synthesis rates.
Fig 9.
Stochastic vs. deterministic simulation trajectories in the response to low (2 Gy), intermediate (4 Gy) and high (8 Gy) irradiation doses.
Single-cell stochastic trajectories—thin color lines; average over 1000 stochastic trajectories—bold black line; deterministic approximation—bold red line.
Fig 10.
Fraction of apoptotic cells as a function of irradiation dose for two types of stochastic simulations.
For each of analyzed doses the fraction and corresponding error was calculated based on 5000 stochastic single-cell simulations. The state of the cell was checked at 72. hour after irradiation which, as shown in Fig 11, is sufficient for unanimous cell fate decision.
Fig 11.
Analysis of the cell fate decision-making process.
(A) PTEN levels in subpopulations of surviving (blue) and apoptotic (red) cells after 4-Gy irradiation. 10 000 cells are simulated in total. (B) Kolmogorov—Smirnov statistics between distributions of six variables which characterize surviving and apoptotic cells.
Fig 12.
Chemotherapeutic agents targeting the p53 regulatory core.
A selection of chemical compounds, both clinically approved chemotherapeutic drugs and newly discovered inhibitors, are shown. Some agents have pleiotropic effects (gemcitabine, 5-fluoroacil); several p53 inhibitors may be effective only towards a mutated, conformationally disrupted p53 (PRIMA-1 and similar not shown); tenovins have activating influence on p53 because they inhibit p53 inhibitor, sirtuin. Nutlins, MIs and RITA inhibit Mdm2 and p53 interaction.