Two-phase dynamics of p53 in the DNA damage response

Xiao-Peng Zhang, Feng Liu, and Wei Wang
PNAS May 31, 2011 108 (22) 8990-8995; https://doi.org/10.1073/pnas.1100600108

  1. Edited* by José N. Onuchic, University of California, La Jolla, CA, and approved April 21, 2011 (received for review January 12, 2011)

Abstract

The tumor suppressor p53 mainly induces cell cycle arrest/DNA repair or apoptosis in the DNA damage response. How to choose between these two outcomes is not fully understood. We proposed a four-module model of the p53 signaling network and associated the network dynamics with cellular outcomes after ionizing radiation. We found that the cellular response is mediated by both the level and posttranslational modifications of p53 and that p53 is activated in a progressive manner. First, p53 is partially activated by primary modifications such as phosphorylation at Ser-15/20 to induce cell cycle arrest, with its level varying in a series of pulses. If the damage cannot be fixed after a critical number of p53 pulses, then p53 is fully activated by further modifications such as phosphorylation at Ser-46 to trigger apoptosis, with its concentration switching to rather high levels. Thus, p53 undergoes a two-phase response in irreparably damaged cells. Such combinations of pulsatile and switch-like behaviors of p53 may represent a flexible and efficient control mode, avoiding the premature apoptosis and promoting the execution of apoptosis. In our model, p53 pulses are recurrently driven by ataxia telangiectasia mutated (ATM) pulses triggered by DNA damage. The p53-Mdm2 and ATM-p53-Wip1 negative feedback loops are responsible for p53 pulses, whereas the switching behavior occurs when the p53-PTEN-Akt-Mdm2 positive feedback loop becomes dominant. Our results suggest that a sequential predominance of distinct feedback loops may elicit multiple-phase dynamical behaviors. This work provides a new mechanism for p53 dynamics and cell fate decision.

The tumor suppressor p53 is at the hub of cellular signaling networks that are activated by stress signals including DNA damage (1). In unstressed cells, p53 is kept at low levels by its negative regulator Mdm2 (2). Upon DNA damage, p53 is stabilized and activated to function primarily as a transcription factor, regulating expression of downstream target genes. This leads to different cellular outcomes such as cell cycle arrest and apoptosis (3); the former facilitates DNA repair and promotes cell survival, whereas the latter provides an efficient way to remove irreparably damaged cells. However, the mechanism for p53-mediated cell fate decision between life and death is not fully understood.

It is known that p53 responds to DNA damage in various modes, depending on cell and stress types (1). Previously, it was proposed that low levels of p53 induce cell cycle arrest, whereas high levels of p53 induce apoptosis (4). Such an analog mode is consistent with the fact that p53 binds to proarrest genes with high affinities but associates with proapoptotic genes with low affinities (5). Recently, it was reported that p53 levels can vary in a series of discrete pulses; in this digital mode, the number of p53 pulses is positively related to the amount of DNA damage (6). Much work has explored the feedback mechanism of p53 oscillations (7–10). The p53-Mdm2 negative feedback loop is recognized as the basis of p53 oscillation (7), and additional positive feedback loops may make p53 oscillations more robust (8). On the contrary, it was suggested that the p53-PTEN (phosphatase and tensin homolog)-Akt-Mdm2 positive feedback loop may terminate oscillations by disrupting the p53-Mdm2 loop (9). Most recently, Batchelor et al. have shown that the ATM (ataxia telangiectasia mutated)-p53-Wip1 (wild-type p53-induced phosphatase 1) negative feedback loop is required for the generation of uniform p53 pulses (10). Therefore, it is important to further clarify how p53 pulses are initiated. Moreover, it is worth noting that p53 pulses were typically observed in MCF-7 human breast cancer cells (6), in which the PTEN gene cannot be expressed because of its promoter methylation (11). By contrast, PTEN can be transactivated by p53 in several cell lines including MCF-10A nontumorigenic mammary epithelial cells (12, 13). This raises the issue of whether p53 pulses can persist throughout the response in normal cells such as MCF-10A cells, because PTEN is induced late in the cellular response (12) and the p53-PTEN-Akt-Mdm2 loop may terminate p53 oscillations (9).

The physiological functions of p53 pulses have recently been explored (8, 14). It was suggested that the cell fate between survival and death may be determined by counting the number of p53 pulses. The strength of DNA damage is repeatedly evaluated; the cell survives after transient p53 pulses, or apoptosis is induced by sustained p53 pulses. This may represent a reliable and flexible mechanism; for example, it can avoid the premature apoptosis resulting from large accidental fluctuations in p53 levels (15). Nevertheless, it may take several hours to initiate apoptosis by p53 pulses even after a decision is taken favoring the death (14). By comparison, high constant levels of p53 may trigger apoptosis quickly once a choice is made in irreparably damaged cells. Therefore, it is tempting to explore whether both the analog and digital modes of p53 activation are exploited in one cellular response.

Motivated by the above considerations, we developed a four-module model to examine the connection between the dynamics of the p53 network and the DNA damage response. The model can depict the whole process from the generation and repair of DNA damage to the determination of cell fate between life and death. For repairable DNA damage, there is only one phase in p53 dynamics: A few pulses are produced before the damage is fixed. For irreparable DNA damage, there exist two phases: The concentration of p53 first shows a series of pulses and then switches to high constant levels, and apoptosis ensues. Thus, the analog and digital response modes are combined to guarantee a reliable decision and quick induction of apoptosis. We also stressed that the ATM-p53-Wip1 loop is essential for the generation of p53 pulses and that the level of PTEN determines whether p53 acts as a pulse generator or a switch in the second phase. Our results are in good agreement with experimental observations and may provide clues to p53-based cancer treatment.

Model and Methods

The response of the p53 network to DNA damage can be envisioned as a signal transduction process (16). We constructed an integrative model of the p53 network composed of four modules: a DNA repair module, an ATM sensor, a p53-centered feedback control module, and a cell fate decision module (Fig. 1). Three important feedback loops are included, namely the p53-Mdm2, ATM-p53-Wip1, and p53-PTEN-Akt-Mdm2 loops, which have been suggested to regulate p53 activity significantly (7, 9, 10).

Fig. 1.
Fig. 1.

Schematic depiction of the integrative model. The model is composed of four modules, separately characterizing the DNA repair, ATM sensor, p53-centered feedback control, and cell fate decision. Four feedback loops are considered, i.e., the p53-Mdm2 and the p53-Wip1-ATM negative feedback loop, and the p53-PTEN-Akt-Mdm2 and the CytoC-Casp3 positive feedback loop. The transactivation of target genes by p53 is denoted by dotted lines. State transition is represented by arrow-headed solid lines, and the promotion and inhibition of state transition are separately denoted by circle-headed and bar-headed lines. Other processes are depicted by arrow-headed double lines.

Our model is able to characterize the process from the generation and repair of DNA damage to the choice of cell fate. Upon ionizing radiation (IR), double-strand breaks (DSBs) are produced and DNA repair proteins are quickly recruited to break sites, forming DSB–protein complexes (DSBCs) (17). For a population of cells exposed to the same radiation dose of DIR, the initial numbers of DSBs are assumed to obey a Poisson distribution with a mean of 35 × DIR (18). Because repair proteins are much fewer than DSBs in most cases (7), we assume that there are 20 repair proteins per cell. ATM is activated by DNA damage through auto-phosphorylation, transiting from inactive dimer (ATM2) to phosphorylated monomer (ATM∗) (19). Subsequently, p53 is stabilized and activated by phosphorylation (20), converting from inactive p53 to active p53∗. Active p53 induces expression of Mdm2, which in turn targets p53 for degradation, enclosing a negative feedback loop (2). Only nuclear p53 is considered here, whereas three forms of Mdm2 are included, namely Mdm2c (unphosphorylated cytoplasmic form), Mdm2cp (phosphorylated cytoplasmic form), and Mdm2n (nuclear form).

Based on its different phosphorylation status, active p53 can be further distinguished between p53 arrester and p53 killer, separately inducing cell cycle arrest and apoptosis (21). For simplicity, here p53 arrester refers to p53 primarily phosphorylated at Ser-15 and Ser-20, whereas p53 killer is p53 further phosphorylated at Ser-46. It is assumed that p53 arrester transactivates p21, Wip1, and p53DINP1 (p53-dependent damage inducible nuclear protein 1), whereas p53 killer transactivates p53DINP1, p53AIP1 (p53-regulated apoptosis-inducing protein 1), and PTEN (12, 21–24). The conversion between p53 arrester and p53 killer is controlled by Wip1 and p53DINP1 (22, 23). As a phosphatase, Wip1 promotes the dephosphorylation of ATM∗ (25). Thus, there exists a negative feedback between ATM and p53 arrester via Wip1. Phosphorylated Akt (Akt∗) promotes the nuclear translocation of Mdm2 by phosphorylating Mdm2c (26). The phosphorylation of Akt is phosphatidylinositol 3,4,5-trisphosphate (PIP3)-dependent (27). On the other hand, PTEN promotes the transition from PIP3 to PIP2 (phosphatidylinositol 4,5-biphosphate) (28). Thus, there exists a double-negative feedback loop involving p53 killer, PTEN, Akt, and Mdm2.

The downstream targets of p53 directly control cellular outcomes. Among them, p21 induces cell cycle arrest, whereas p53AIP1 promotes apoptosis by inducing the release of mitochondrial cytochrome c (CytoC) into the cytoplasm (21). Released CytoC then activates caspase 3 (Casp3), and apoptosis ensues. A positive feedback between CytoC release and Casp3 activation is considered here (29). This feedback loop is crucial for the irreversible apoptosis induction, and similar irreversibility owning to positive feedback loops is exploited in stem cell differentiation (30). For simplicity, we did not model the formation of apoptosomes and activation of caspase 9 (31); rather, the persistent activation of Casp3 is considered the marker of apoptosis here.

The model implementation details are presented in SI Appendix. The process of DNA repair was simulated by the Monte Carlo method based on the two-lesion kinetic model (7, 32) (see SI Appendix, Supplemental Method S1). The dynamics of proteins in the other modules are characterized by ordinary differential equations (see SI Appendix, Supplemental Method S2). Eqs. S1–S19 characterize the dynamics of three p53-centered feedback loops, and Eqs. S20–S23 characterize the dynamics of p21, p53AIP1, CytoC, and Casp3. Specifically, the ATM-dependent activation of p53 and Mdm2-mediated degradation of p53 (Eqs. S5–S7), together with the conversion between p53 arrester and p53 killer mediated by Wip1 and p53DINP1 (Eqs. S15 and S16), are key steps in regulating p53 activity. The definition of each variable and parameter values are listed in Tables S1 and S2, respectively. The bifurcation diagrams were plotted by using the free softwares XPPAUT and Oscill8. The units of time and radiation dose are minute and Gy, respectively, and the units of other parameters ensure that the concentrations of proteins are dimensionless.

Results

Overview of the Dynamics of the p53 Network.

We first present an overview of the network dynamics by displaying the output of each module at two typical radiation doses in Fig. 2. The number of DSBCs, nc, indicates the presence of DNA damage. nc quickly rises to its maximum (i.e., the number of repair proteins per cell) upon DNA damage and stays there until the number of DSBs falls below 20.

Fig. 2.
Fig. 2.

Overview of the dynamics of the p53 network. Time courses of nc and the levels of ATM∗, p53∗, p21, and Casp3 at DIR = 3 Gy (A) or 5 Gy (B).

At DIR = 3 Gy, the concentrations of ATM∗, p53∗, and p21 undergo three pulses followed by basal levels, whereas Casp3 level remains low (Fig. 2A). Accordingly, the cell cycle is first arrested by p21, and the cell recovers to normal proliferation after DNA damage is fixed. At DIR = 5 Gy, four pulses are first produced in ATM∗, p53∗, and p21 levels; then the concentrations of ATM∗, p53∗, and Casp3 quickly rise to high levels (at different rates), whereas p21 returns to basal levels (Fig. 2B). In this case, the cell undergoes apoptosis. Thus, the cellular response to irreparable DNA damage is divided into two phases. In the first phase, the cell cycle arrest allows time to fix DNA damage, and the cell repeatedly checks for the presence of DSBs via oscillations in protein levels. This provides a robust mechanism for committing the cell to apoptosis, avoiding unnecessary death (15). If the damage is not fixed after four pulses, the apoptotic decision is taken, and the caspase cascade is quickly initiated in the second phase.

Therefore, depending on the amount of DNA damage, the network may exhibit the one- or two-phase dynamics; the first and the second phase are characterized by pulsatile and switch-like behaviors of p53, respectively. As a result, a reliable choice is made between life and death, and apoptosis is quickly induced once necessary. Such a two-phase mode of p53 response may represent an optimal mechanism, having advantages over the purely analog or digital control mode mentioned above.

Recurrent Initiation of p53 Pulses by ATM Pulses.

It is worthy to clarify the contributions of different feedback loops to the generation of p53 pulses. Here, we mainly investigated the effects of two negative feedback loops, namely the p53-Mdm2 and the ATM-p53-Wip1 loop (because PTEN is induced during the late phase (12), we can ignore the positive feedback loop involving PTEN in this section). It is important to determine whether both the loops are indispensable for p53 pulses.

Fig. 3A shows the bifurcation diagram of ATM∗ level versus nc. ATM∗ level remains low for small nc, and a Hopf bifurcation appears near nc = 7, beyond which ATM∗ level can undergo repeated oscillations with nearly the same amplitude over a wide range of nc. That is, such minor DNA damage as caused by the IR of 0.2 Gy can be sensed by ATM (19); thus, ATM acts as a sensitive and reliable detector of IR-induced DNA damage.

Fig. 3.
Fig. 3.

Initiation of p53 pulses by ATM pulses. (A–B) The bifurcation diagram of ATM∗ level vs. nc (A) and that of ATM∗ level vs. kswip1 (B) with nc = 20. The stable and unstable steady states are indicated by thick and thin black lines, respectively. The minima and maxima of the limit cycles are denoted by open circles. (C) A single pulse in the levels of p53∗, ATM∗, and Wip1 at DIR = 1 Gy. (D) Time course of p53∗ level with kswip1 = 0 or 0.2 at DIR = 4 Gy. (E) The bifurcation diagram of p53∗ level vs. ksmdm2 with nc = 20. The same convention is used as in panels A and B. (F) The parameter plane spanned by kswip1 and ksmdm2 is divided into two regions, separately corresponding to oscillatory and nonoscillatory behaviors of p53.

The ATM oscillations depend remarkably on Wip1, which is regulated mainly by p53. We plotted the bifurcation diagram of ATM∗ level versus the p53-inducible synthesis rate of Wip1, kswip1, to characterize the effect of Wip1 on the generation of ATM oscillations (Fig. 3B). For kswip1 < 0.0585, ATM∗ level settles in a higher steady state (the other two steady states are unstable). When kswip1≥0.0585, ATM∗ level can undergo oscillations, and the amplitude drops with increasing kswip1. Thus, a sufficient amount of Wip1 is required for ATM oscillations, whereas excessive Wip1 tends to reduce the amplitude of oscillation. Our results are consistent with the experimental observations that removal of Wip1 leads to high levels of phosphorylated ATM and that overexpression of Wip1 leads to reduction in ATM phosphorylation (10).

The ATM-p53-Wip1 loop with an intrinsic time delay is important for the generation of p53 pulses. Over one period, ATM∗ level first rises, and p53 then gradually accumulates to a peak level, accompanied by an increase in Wip1 level (Fig. 3C). Wip1 then inhibits ATM∗ activity, and its level drops quickly. After a delay, p53∗ level also falls, while Wip1 level decreases at a slower rate. Note that ATM can be reactivated by residual DNA damage, and p53 is subsequently activated again. Thus, p53 pulses are recurrently driven by ATM pulses, which is in agreement with the experimental findings (10). Moreover, owing to stochasticity in the generation and repair of DNA damage, there exists considerable variability in the responses of individual cells to the same IR, as seen in the time courses of ATM∗ and Wip1 levels for three cells at DIR = 5 Gy (Fig. S1).

Fig. 3D displays the temporal evolution of p53∗ level with different kswip1. For kswip1 = 0, that is, the ATM-p53-Wip1 loop is shut off, the concentration of p53∗ converges to a constant level during the repair of DNA damage. For kswip1 = 0.2, however, four pulses are still generated although the amplitude becomes lower. Therefore, the ATM-p53-Wip1 loop is necessary for the generation of p53 pulses.

We further examined the role of the p53-Mdm2 loop in the generation of p53 pulses, focusing on the influence of the p53-inducible synthesis rate of Mdm2, ksmdm2. In the bifurcation diagram (Fig. 3E), p53∗ level stays in an upper steady state (the middle and lower steady states are unstable) for ksmdm2≥0.178. Only when ksmdm2 < 0.178 can pulses be evoked, and the amplitude drops with increasing ksmdm2 over a wide range. Notably, the presence of p53 oscillations at ksmdm2 = 0 indicates that disrupting the p53-Mdm2 loop does not terminate p53 oscillation. The temporal evolution of p53∗ level with different ksmdm2 is consistent with Fig. 3E (Fig. S2A). Whereas the concentration of p53∗ slowly converges to a constant level in a damped-oscillation manner at ksmdm2 = 0.2, four p53 pulses are induced at ksmdm2 = 0. This implies that the p53-Mdm2 loop becomes redundant for p53 oscillations when the ATM-p53-Wip1 loop is present. We also assessed the role of the p53-Mdm2 loop in the induction of p53 pulses in the model proposed by Batchelor et al. (10), where an explicit time delay was introduced (Fig. S2B). Similarly, there appear several p53 pulses in the absence of p53-induced Mdm2 expression. Therefore, the p53-Mdm2 loop may be dispensable for the generation of p53 pulses in the presence of another negative feedback loop.

On the kswip1-ksmdm2 parameter plane, the p53 dynamics are divided into oscillatory and nonoscillatory regimes (Fig. 3F). To generate p53 oscillations, the ATM-p53-Wip1 loop must be present with kswip1 > 0.0585; the area of oscillation region almost linearly enlarges with increasing kswip1. By contrast, enhancing the expression of Mdm2 shrinks the oscillation region. Taken together, these results suggest that the ATM-p53-Wip1 loop is essential for the generation of p53 pulses, whereas the p53-Mdm2 loop may have a role in fine tuning the shape of p53 pulses.

Two-Phase Dynamics of the Network.

Here, we reveal the dynamics of several proteins in the p53 network. Fig. 4A displays the temporal evolution of p53∗, Mdm2n, Mdm2c, Akt∗ and PTEN levels at DIR = 3 Gy. Three p53 pulses are triggered during the repair of DNA damage. The intervals between successive pulses are about 6 hr, and the amplitudes are almost invariable, consistent with the experimental observations of digital p53 pulses (6). Because PTEN is expressed only at basal levels, most of Mdm2 is phosphorylated by active Akt and enters the nucleus. Thus, only a small amount of Mdm2 remains in the cytoplasm. After the cell recovers to normal proliferation, p53∗ returns to basal levels, whereas Akt∗ level remains constant and Mdm2n level is significantly larger than zero.

Fig. 4.
Fig. 4.

Temporal evolution of the levels of proteins in the p53-centered feedback loops at DIR = 3 Gy (A) or 5 Gy (B).

At DIR = 5 Gy, the dynamics of the proteins undergo two phases (Fig. 4B). In the first phase, four pulses are produced in p53∗ and Mdm2n levels, while active Akt stays at constant levels without PTEN induction. During the second phase, Akt is deactivated by PTEN, which accumulates and reaches a constant level. Thus, the concentration of p53∗ switches to a rather high level because the nuclear entry of Mdm2 is blocked. Notably, p53 and Akt counteract each other. Our results are also consistent with the findings that PTEN becomes remarkable only during the late phase of the cellular response to IR (12). The two-phase p53 dynamics result from two aspects of regulation: The loss of Wip1 induction relieves its inhibitory effect on ATM, elevating p53 level, and the full activation of p53 by PTEN further drives p53 to rather high levels by sequestering Mdm2 in the cytoplasm. Such a two-phase dynamical behavior of the p53 network awaits experimental identification.

Dynamics and Functions of p53 Arrester and p53 Killer.

We further investigated the dynamics of p53 arrester and p53 killer, which are directly associated with the ultimate cell fate. At DIR = 3 Gy, only pulses of p53 arrester and its downstream targets are triggered (Fig. S3A). At DIR = 5 Gy, p53 arrester shows four pulses in the first phase and then remains at basal levels, whereas the concentration of p53 killer switches from basal levels to high levels in the second phase (Fig. 5A and Fig. S3B). Thus, p53 arrester and p53 killer predominate in the first and the second phase, respectively. The p53 arrester transactivates Wip1, p53DINP1, and p21, which induces cell cycle arrest in the first phase. The p53 killer induces PTEN, p53DINP1, and p53AIP1, which are proapoptotic, and thus apoptosis will be initiated in the second phase (Fig. 5B). The transition between p53 arrester and p53 killer is controlled by Wip1 and p53DINP1; the conversion occurs when the temporal integration of p53DINP1 reaches a certain threshold. Moreover, because the stochasticity in the generation and repair of DNA damage is transmitted to downstream modules, the dynamics of two forms of active p53 and their downstream targets are also variable from cell to cell (Fig. S4).

Fig. 5.
Fig. 5.

Dynamics of two forms of active p53 and their downstream targets. (A) Time courses of the levels of p53 arrester (black) and p53 killer (red) at DIR = 5 Gy. (B) Temporal evolution of the levels of p21 (black), Wip1 (red), p53DINP1(green), PTEN (cyan), p53AIP1 (purple), and Casp3 (blue) at DIR = 5 Gy. (C–D) Time courses of the concentrations of p53 arrester (black), p53 killer (red), and Casp3 (blue) with kswip1 = 0 and DIR = 1 Gy (C) or kswip1 = 0.092 and DIR = 10 Gy (D). (E) The number of pulses in p53 arrester preceding apoptosis induction, nar, as a function of kswip1. (F) The fraction of apoptotic cells in a population of 2,000 cells, FA, vs. DIR with kswip1 = 0 (red), 0.09 (black), or 0.092 (blue).

In the following, we systematically explored how Wip1 affects the radiosensitivity of cells via modulating the conversion between p53 arrester and p53 killer. Without p53-inducible synthesis of Wip1 (kswip1 = 0), p53 killer is induced quickly after one pulse of p53 arrester, and apoptosis is triggered soon even at DIR = 1 Gy (Fig. 5C). That is, Wip1-deficient cells become ultrasensitive to irradiation. This is consistent with the role of Wip1 as an oncogenic regulator in stress-induced apoptosis (33). By contrast, in Wip1-proficient cells it takes a long time for p53 killer to predominate over p53 arrester even at DIR = 10 Gy (Fig. 5D). Thus, the induction of apoptosis is significantly postponed, and the cell becomes resistant to irradiation when Wip1 is overexpressed. This may partially explain how Wip1 acts as an oncogene and why it is frequently overexpressed in several cancers (33). The marked influence of Wip1 levels on the radiosensitivity of cells results form its role in preventing the primary activation of p53 via ATM and further activation by attenuating its phosphorylation at Ser-46 (22).

We also examined how the number of pulses in p53 arrester required for apoptosis induction, nar, varies with kswip1. When kswip1 < 0.07, apoptosis is triggered after a single pulse of p53 arrester at DIR = 1 Gy (Fig. 5E). But nar rises remarkably when kswip1≥0.07. That is, high levels of Wip1 slow down the convention from p53 arrester to p53 killer. Thus, the transition between p53 arrester and p53 killer is significantly influenced by the level of Wip1. Moreover, the effects of other parameters involved in the ATM-p53-Wip1 loop on the robustness of the two-phase dynamics of p53 are characterized in Table S3.

As reported above, the responses of individual cells exhibit remarkable variability even when they are exposed to the same IR. The fraction of apoptotic cells, FA, versus DIR was plotted to exhibit the effect of Wip1 on cell fate decision at the population level (Fig. 5F). The curves look like a sigmoidal function. In the normal case, apoptosis first appears at DIR = 4 Gy, and all cells die at DIR = 7.5 Gy. In the Wip-deficient case, the curve shifts leftward, and apoptosis first appears at DIR = 0.2 Gy and all cells die at DIR = 0.9 Gy. When Wip1 is overexpressed, however, the curve shifts rightward, and apoptosis first appears at DIR = 7 Gy. That is, cells become resistant to stress signals. Taken together, Wip1 has a marked effect on cell fates and may be an important target of cancer therapy.

The Role of PTEN in p53-Mediated Cell Fate Decision.

We have demonstrated that Wip1 has a key role in generating p53 pulses during the first phase, whereas PTEN contributes to full activation of p53 in the second phase. The effect of PTEN on p53 activity and cell fate decision is further characterized in detail in this section.

Fig. 6A displays the bifurcation diagram of p53∗ level versus the p53-inducible synthesis rate of PTEN, ksPTEN. For ksPTEN < 0.093, p53∗ remains in a low steady state. When 0.093 ≤ ksPTEN < 0.119, oscillations can be evoked in p53∗ level. For 0.119 ≤ ksPTEN < 0.155, p53∗ level settles in an upper steady state (the other two steady states are unstable). When ksPTEN≥0.155, p53∗ remains at high levels. Thus, PTEN significantly affects the dynamics of p53 in the second phase. Moreover, the influences of other parameters involved in the p53-PTEN-Akt-Mdm2 loop on the robustness of p53 dynamics are further analyzed in Table S3.

Fig. 6.
Fig. 6.

Effect of PTEN on p53 dynamics and cell fate decision. (A) The bifurcation diagram of p53∗ level vs. ksPTEN with nc = 20. The stable and unstable steady states are indicated by thick and thin black lines, respectively. The minima and maxima of the limit cycles are denoted by open circles. (B) Time courses of the levels of p53 killer and Casp3 with ksPTEN = 0 (blue), 0.105 (red), or 0.2 (black). (C) The fraction of apoptotic cells in a population of 2,000 cells vs. ksPTEN at DIR = 5 Gy. The inset is a zoom in of the curve. (D) The histograms of timing of apoptosis induction, TA (defined as the time point of Casp3 activation), with ksPTEN = 0.015 or 0.2. The time bin is 20 min.

Considering that p53 killer is the dominant form of p53∗ in the second phase and its level is close to p53∗ level, here we investigated only the temporal evolution of p53 killer with different ksPTEN. Clearly, p53 killer converges to a lower level after damped oscillations at ksPTEN = 0, and Casp3 cannot be activated (Fig. 6B). For an intermediate value of ksPTEN, p53 killer shows a series of pulses, and Casp3 is activated to trigger apoptosis. As expected, p53 killer quickly rises to a high level at ksPTEN = 0.2, and Casp3 is activated fast. Note that PTEN affects the network dynamics by modulating the relative predominance of the p53-PTEN-Akt-Mdm2 loop over the p53-Mdm2 loop because it inhibits the nuclear translocation of Mdm2 (26). Only when the strength of these two loops becomes comparable, they cooperate to trigger p53 pulses (34). In the other cases, p53 remains at low or rather high levels, depending on which loop predominates.

We also explored the effect of PTEN on apoptosis induction at the cell population level (Fig. 6C). Apoptosis first appears at ksPTEN = 0.1, and the fraction of apoptotic cells, FA, gets saturated when ksPTEN > 0.2. Moreover, there exists only a slight difference in FA between the cases separately with ksPTEN = 0.105 and 0.2 (Fig. 6C, Inset). We further investigated the influence of PTEN on the timing of apoptosis induction (Fig. 6D). Almost all apoptosis is initiated around 1,520 min for ksPTEN = 0.2 (the irradiation is applied at time 0). For ksPTEN = 0.105, besides the main peak around 1,600 min, two other peaks separately appear near 1,900 and 2,150 min, indicating that apoptosis is induced after two or three pulses of p53 killer. In this case, about 60% of the apoptosis happens after one pulse of p53 killer. Thus, there exists more variability in apoptosis induction mediated by pulses of p53 killer, whereas quick induction of apoptosis evoked by high levels of p53 remarkably reduces the response heterogeneity. Taken together, PTEN is important for killing irreparably damaged cells and may act as another target of cancer therapy.

Discussion

The p53-Mediated DNA Damage Response.

In this work, we constructed an integrative model of the p53 network to clarify the link between p53 dynamics and the DNA damage response. Our results support the notion that p53 is activated in a progressive manner. First, p53 is primarily modified (such as phosphorylation at Ser-15 and Ser-20) and accumulates in pulses to induce protective cell cycle arrest for repairable DNA damage; it is further modified (such as phosphorylation at Ser-46) and fully activated to induce apoptosis for irreparable DNA damage (35). The pulsing behavior of p53 in the first phase exerts a reliable and flexible control, avoiding the premature apoptosis. The high plateau levels of p53 in the second phase guarantee the quick induction of apoptosis after the apoptotic decision is taken. These results clearly demonstrate that both the levels and posttranslational modifications of p53 regulate the cellular response to DNA damage. Moreover, the sequential induction of Wip1 and PTEN by p53 in turn modulates p53 activity by changing the predominance of distinct feedback loops during the response.

Oscillation and Bistability in p53 Dynamics.

There has been much theoretical work on the mechanism of p53 oscillation (7, 8, 14). Moreover, p53 dynamics may also exhibit bistability (36). However, most models ignored the possible association between the oscillatory and bistable behaviors of p53. Puszynski et al. first combined oscillation and bistability in their model (9). Nevertheless, they only considered the p53-Mdm2 loop, which alone can trigger only continuous p53 oscillations rather than discrete p53 pulses as observed experimentally (6). Moreover, the mechanism for apoptosis induction is not robust enough because the higher steady-state levels of p53 are comparable to the peaks of p53 oscillations. In our model, however, the p53 pulses are triggered by ATM pulses, well consistent with experimental observations (10), and rather high levels of p53 are maintained to induce apoptosis. Constrained by experimental data, we ignored intrinsic noise from gene expression, which may be important under some conditions. For example, the intrinsic noise resulting from extinction and resurrection of proteins can induce bistability in the deterministically monostable system (37). In our work, fluctuations in the levels of Wip1 and PTEN owing to intrinsic noise may make p53 dynamics more variable among cells. Thus, it is intriguing to further investigate the effect of intrinsic noise on cell fate decision.

An Optimal Mode of p53 Response to DNA Damage.

It is worth comparing the present work with the previous one on p53 dynamics (14), in which p53 responds to DNA damage only in a series of pulses. The cell fate decision is governed by the number of p53 pulses, which may represent a robust mechanism. But when triggered by proapoptotic p53 pulses, it may take several hours to initiate apoptosis after the decision; this is inefficient in killing irreparable cells. In the present work including the ATM-p53-Wip1 and p53-PTEN-Akt-Mdm2 loops, the two-phase dynamics of p53 occur in irreparably damaged cells. The pulses of p53 induce cell cycle arrest and ensure a reliable choice, whereas high constant levels of p53 promote the quick execution of apoptosis. That is, the advantage of p53 pulses as a molecular timer for decision-making is retained, whereas the deficiency with p53 pulses in apoptosis induction is overcome in the current work. We also demonstrated how Wip1 and PTEN can remarkably regulate p53 dynamics. Moreover, the underlying connection between p53 dynamics and cellular outcomes is clearly clarified. In sum, the two-phase mode of p53 response may represent an optimal mechanism, taking advantage of the benefits of both the digital and analog modes.

Plausibility of the Two-Phase Dynamics of p53.

The two-phase dynamics of the p53 network are compatible with experimental observations. It was reported that Wip1 and PTEN are induced by p53 during the early and late phases of the cellular response, respectively (12, 24). Thus, the ATM-p53-Wip1 loop may cooperate with the p53-Mdm2 loop to elicit p53 pulses in the early phase, whereas the p53-PTEN-Akt-Mdm2 loop may become dominant later and drive p53 to high levels (Fig. S5). Our results are consistent with the finding that it is p21 rather than the proapoptotic proteins that undergoes pulses in the DNA damage response (10). Moreover, it is worthy to note that typical p53 pulses were experimentally observed in the transformed MCF-7 cells, in which PTEN cannot be expressed because of methylation in its promoter (11). It is expected to validate the two-phase dynamics of p53 in MCF-10A cells, in which the above three feedback loops are all intact, or by transfecting MCF-7 cells with PTEN under the control of p53-responsive promoter. Furthermore, it is promising to explore the multiple-phase dynamics in other systems like the sporulation-competence decision system, in which there exist three stages in the decision-making process (38).

Implications of p53 Dynamics in Cancer Treatment.

The two-phase model of p53 activity may provide clues to cancer treatment. Our results suggest that p53 pulses play a prosurvival role by inducing cell cycle arrest and facilitating DNA repair. We propose that sustained p53 pulses may extensively exist in cancer cells with proficient Wip1. Thus, RNA inference may be exploited to reduce Wip1 expression in those cells so that they can be killed quickly by shortening the protective cell cycle arrest. On the other hand, PTEN contributes to apoptosis induction by fully activating p53. Thus, reactivation of PTEN in some cancer cells may greatly enhance the p53-dependent apoptosis and improve the treatment efficiency. Therefore, our work suggests that regulation of p53 dynamics may be an efficient way to improve the therapy efficacy.

Acknowledgments

This work was supported by the National Basic Research Program of China (2007CB814806), the National Natural Science Foundation of China (10834002), the Natural Science Foundation of Jiangsu Province (BK2009008), and the Program for New Century Excellent Talents in Universities (NCET-08-0269).

Footnotes

  • 1To whom correspondence may be addressed. E-mail: fliu{at}nju.edu.cn or wangwei{at}nju.edu.cn.

Freely available online through the PNAS open access option.

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Two-phase dynamics of p53 in the DNA damage response
Xiao-Peng Zhang, Feng Liu, Wei Wang
Proceedings of the National Academy of Sciences May 2011, 108 (22) 8990-8995; DOI: 10.1073/pnas.1100600108
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