Stimulus- and cell type-dependent p53 dynamics
To experimentally profile the differential signaling outputs of p53 pathway, we used single-cell p53 dynamics acquired from live-cell imaging as the quantitative signaling readouts. We activated p53 and the p53 pathway by three different anticancer drugs. The DNA damaging drug, Etoposide, is a topoisomerase inhibitor and activates the DNA damage signaling kinase, ATM, which then phosphorylates both p53 and Mdm2, subsequently attenuating the inhibitory p53-Mdm2 interaction that enables p53 induction [22, 23] (Fig. 1A). The Mdm2 inhibitor, Nutlin-3a, directly abrogates the binding of Mdm2 to p53, thus allowing p53 level to increase [24, 25] (Fig. 1B). The anti-metabolite chemotherapeutic, 5-fluorouracile (5-FU), is a pyrimidine analog that interferes with DNA and RNA synthesis [26]. Although 5-FU induces both DNA and RNA damage, increasing evidence suggests that p53-mediated 5-FU cytotoxicity is mainly triggered by impairment of the ribosomal biosynthesis in the nucleoli [27]. Such nucleolar stress activates the translocation of ribosomal proteins, such as RPL11 and RPL5, to bind and sequester Mdm2, leading to p53 upregulation [28,29,30] (Fig. 1C). In addition to the different drugs, we also characterized the cell-type variation in p53 pathway response by employing five p53 reporter cancer cell lines that we generated and studied before, including A549 (lung), U-2 OS (bone), A375 (skin), MCF7 (breast), and 769-P (kidney) [15]. These cell lines were engineered to stably express a p53-Venus construct (i.e., wild-type p53 tagged with a yellow fluorescent protein, Venus) [11, 14]. Time-lapse imaging of the respective clonal fluorescent reporter lines allows us to obtain real-time p53 dynamics in individual cells via the fluorescence signal of p53-Venus, which is mostly localized in the nucleus. Representative still images and the quantified time courses of the average nuclear p53-Venus fluorescence that the majority of the cell population exhibited at each drug concentration are shown in Fig. 1 (middle and right panels) for the selected three drugs and five cancer cell lines.
The single-cell data revealed both stimulus- and cell type-dependent characteristics in the dose responses of p53 dynamics (Fig. 1 and Additional file 1: Figure S1). At low dose, Etoposide, Nutlin-3a, and 5-FU all triggered periodic pulsing of p53 in all five cell lines, although some cell lines and drugs appeared to engender more regular periodic pulsing (e.g., A549 under 1 μM Etoposide). Upon increasing drug concentrations, p53 induction changed to different dynamic modes that varied between both the drugs and cell lines. Under Etoposide, the cell population switched to either monotonic induction of p53 (A549, U-2 OS, and A375) or an extended large p53 pulse (MCF7 and 769-P), without exhibiting alternative transitional dynamics between the low- and high-drug concentrations (Fig. 1A, right panel). In contrast, responses to Nutlin-3a showed a distinctive transitional mode of p53 dynamics at the intermediate drug doses in A549, U-2 OS, and 769-P cells before a further change to the saturating, high-drug mode. Specifically, for these three cell lines, intermediate concentrations of Nutlin-3a (10–50 μM) activated an initial p53 pulse followed by approximately exponential upregulation of p53, a novel p53 dynamic mode not observed before (Fig. 1B, right panel). As Nutlin-3a concentration further increased, the initial p53 pulse diminished and p53 induction kinetics were largely exponential. Dose responses to 5-FU revealed yet another new mode of transitional dynamics in A549, A375, and 769-P, in which the initial p53 pulse was followed by an elevated plateau of p53 level that was lower than the amplitude of the initial pulse (Fig. 1C).
In addition to drug-dependent variability, significant cell-type variation in p53 responses was also observed between the five cell lines in response to the same drug that correlated with alternative cell fate outcome of cell cycle arrest and cell death. Figure 2 summarizes the fraction of cells that exhibited the different p53 dynamic modes and then went into cell cycle arrest (upper panel) or cell death (lower panel). p53 dynamics induced by Etoposide exhibited two distinct dose-response phenotypes that varied between cell types: one was from p53 pulsing at low drug concentrations to monotonic induction at high-drug concentrations (A549, U-2 OS, A375), and the other was from pulsing to an extended large pulse (MCF7 and 769-P). We have previously shown that the monotonic induction mode, which resulted in a high level of p53 upregulation, promoted drug-induced cell death, while the extended large pulse mode restrained p53 upregulation at a low level and led to mostly cell cycle arrest, rendering MCF7 and 769-P resistant to Etoposide-induced cell death even at high drug concentrations [15] (Fig. 2A). Treatment of Nutlin-3a and 5-FU resulted in five different dose-response phenotypes of p53 dynamics, including the unique transitional dynamic modes as discussed above as well as the two saturating dynamic modes as seen for Etoposide. We again observed a strong correlation between the monotonic/exponential induction mode of p53 that resulted in high p53 upregulation levels with the cell fate outcome of cell death as well as the correlation of the p53 pulsing mode with cell cycle arrest (Fig. 2B, C). Interestingly, MCF7 cells showed largely the same dose-dependent p53 dynamics in response to all three drugs, despite the different mechanisms of action of the drugs, suggesting that MCF7 may have evolved to regulate p53 upregulation by one dominant regulatory motif. Moreover, MCF7 exhibited the extended large pulse mode of p53 dynamics at saturating high concentrations of all three drugs, which led to mostly cell cycle arrest and resistance to drug-induced cell death, except for high concentrations of Nutlin-3a. In contrast, A549 and 769-P cells showed three distinctive dose responses of p53 dynamics to the three different drugs, indicating their functional dependence on a more diverse set of p53 regulatory motifs that could be potentially exploited, e.g., to confer drug selectivity. For instance, 769-P was resistant to Etoposide-induced cell death due to the suppressive, low p53 upregulation in the form of an extended large pulse. Nonetheless, p53 in 769-P can be upregulated to the high-level, monotonic induction mode by high doses of Nutlin-3a, followed by cell death (Fig. 2B), illustrating that Nutlin-3a is a more effective cytotoxic therapeutic for 769-P. Overall, the striking variability in the dose responses of p53 dynamics exhibited by the different cell lines suggested that p53 activation is regulated not only by variable drug mechanisms but also the cellular contexts of the mammalian cells, which likely have evolved differential dependence on selected p53 pathway components and interaction motifs. As the variable p53 levels resulted from the distinct p53 dynamics played a key role in promoting alternative cell fate outcomes of cell cycle arrest and cell death, as we elucidated before [15], it is important to understand the quantitative and mechanistic basis of the differential dynamic outputs of p53 pathway, which we elaborated below.
Dynamic output of the core p53-Mdm2 negative feedback loop
To elucidate, at the network motif level, the mechanistic origin of the stimulus- and cell type-dependent dose response of p53 dynamics that we experimentally observed, we first analyzed the dynamic output of the core p53-Mdm2 negative feedback loop. Etoposide perturbs this negative feedback via phosphorylation and activation of ATM, while Nutlin-3a and 5-FU inhibit Mdm2 directly (Fig. 1, left panel). We performed computational analysis of both regulatory motifs and found their quantitative outputs of p53 dynamics were largely the same. As we already detailed the mathematical formulation of the ATM/p53/Mdm2 module in a previous study [15], here we elaborated the kinetic equations and simulation results in response to Nutlin-3a as a representative scenario. Results for the p53-Mdm2 response to Etoposide by activating the ATM/p53/Mdm2 module are provided in the supplementary materials (Additional file 1: Figure S2).
Dynamic output of the p53-Mdm2 negative feedback in response to Nutlin-3a is formulated by the following delay differential equations (DDEs).
$$\frac{d\left[\mathrm{p}53\right]}{dt}={k}_{\mathrm{p}0}-\frac{k_{\mathrm{mp}}}{1+{k}_{\mathrm{N}}\left[\mathrm{Nutlin}\right]}\left[\mathrm{p}53\right]\left[\mathrm{Mdm}2\right]-{\gamma}_{\mathrm{p}}\left[\mathrm{p}53\right]$$
(1)
$$\frac{d\left[\mathrm{Mdm}2\right]}{dt}={k}_{\mathrm{m}0}+\frac{k_{\mathrm{pm}}{\left[\mathrm{p}53\right]}_{t-{\tau}_{\mathrm{m}}}^4\ }{K_{\mathrm{pm}}^4+{\left[\mathrm{p}53\right]}_{t-{\tau}_{\mathrm{m}}}^4}-{\gamma}_{\mathrm{m}}\left[\mathrm{Mdm}2\right]$$
(2)
where [ ] denotes the dimensionless concentrations of the total proteins (p53 and Mdm2). kp0 (km0) and γp (γm) describe the rate of basal production and degradation of p53 (Mdm2), respectively. kmp is the rate constant of Mdm2-mediated p53 degradation. The transcriptional activation of Mdm2 by the tetrameric p53 is characterized by a Hill function of 4th order with a rate constant kpm, Michaelis parameter Kpm, and time delay τm. [Nutlin] is the concentration of Nutlin-3a in the unit of μM, and kN is the inhibitory strength of Nutlin-3a in attenuating the Mdm2-mediated p53 degradation. We set kN = 0.45 for all of the following simulation analysis, as it produced dose responses largely similar to the experimental data.
We first analyzed how p53 dynamics depended on the different kinetic parameters considered in Eqs. (1) and (2) by numerically simulating the DDEs in a large parameter space. This allowed us to pinpoint parameter sets that can generate periodic pulsing of p53 at 1 μM Nutlin-3a for further analysis. Under all such parameter sets, the simulated dose responses to increasing concentrations of Nutlin-3a produced similar p53 dynamics with a unique mode of transitional dynamics, i.e., an initial p53 pulse followed by an elevated plateau (Fig. 3A). Such transitional dynamics agreed with what we experimentally observed in A549, A375, and 769-P cells under the 5-FU treatment, suggesting that the p53 responses induced by 5-FU in these three cell lines were largely mediated by the central p53-Mdm2 negative feedback loop. However, this mode of p53 transitional dynamics was not observed experimentally for the dose responses to Nutlin-3a or Etoposide. Moreover, we analyzed the distribution of the parameter values that can result in pulsing p53 (Fig. 3B). The rate constants associated with p53 and Mdm2 interactions, including the p53-induced Mdm2 production rate (kpm) and the Mdm2-mediated p53 degradation rate (kmp) were most broadly distributed, spanning over a 30 to 50-fold range. This showed that the p53 pulsing output can be retained over a large variation of these two constants, indicating that the interaction structure of the p53-Mdm2 negative feedback motif largely determines the p53 pulsing output. Comparatively, the value for the Mdm2 basal degradation rates, γm, exhibited the narrowest distribution, though still spanning an 8-fold range. The output of the periodic pulsing mode of p53 is thus likely most sensitive to cellular noise and/or cellular changes that alter this basal degradation rate.
Besides the above rate constants, dynamic output of the p53-Mdm2 negative feedback is also regulated by the time delay, τm, in p53-mediated Mdm2 upregulation. In the above simulations, we set τm = 2.1 hr, similar to most previous modeling analysis. Varying the value of τm had a significant impact, in particular on the oscillatory features of p53 at low drug doses (Fig. 3C). Periodic oscillation of p53 was observed only when τm ≥ 0.9 h. For 0.9 h ≤ τm < 2.3 h, p53 dynamics displayed damped oscillation, while 2.3 h ≤ τm < 4.9 h gave rise to undamped, regular sinusoidal p53 oscillations. For τm ≥ 4.9 h, p53 oscillation became non-sinusoidal, but still maintained the periodicity. Across the whole oscillatory regime, the pulsing period of p53 was found to be linearly proportional to the time delay, τm, and the pulsing amplitude also showed positive dependence on the τm value (Fig. 3C). However, varying τm did not alter the transitional dynamics of p53 generated by the p53-Mdm2 negative feedback as shown in Fig. 3A, again supporting that the interaction structure of the p53-Mdm2 negative feedback determines the dynamic phenotypes of p53 responses.
p53 transitional dynamics conferred by additional positive feedback
To identify additional regulatory components and interactions needed to generate the context-dependent p53 dynamics that we experimentally observed, we first examined the impact of additional positive feedback loops. For simplicity, we chose to analyze the following two generic positive feedback structures, where p53 transcriptionally activates a downstream target gene that positively enhances p53 upregulation either directly (Type 1) or via inhibiting Mdm2 (Type 2) (Fig. 4A). Here, we showed simulation results of the dose-dependent p53 output in response to Nutlin-3a with these two different types of positive feedback loops, as p53 dynamics induced by Nutlin-3a deviated most significantly from the simulated dynamic output of the p53-Mdm2 negative feedback alone. Kinetics of the positive feedback gene, denoted as PF, and its direct activating activity on p53 or inhibitory activity on Mdm2 can be formulated as follows:
$$\frac{d\left[\mathrm{PF}\right]}{dt}={k}_{\mathrm{f}0}+\frac{k_{\mathrm{f}}{\left[\mathrm{p}53\right]}_{t-{\tau}_{\mathrm{f}}}^4\ }{K_{\mathrm{f}}^4+{\left[\mathrm{p}53\right]}_{t-{\tau}_{\mathrm{f}}}^4}-{\gamma}_{\mathrm{f}}\left[\mathrm{PF}\right]$$
(3)
$$\frac{d\left[\mathrm{p}53\right]}{dt}={k}_{\mathrm{p}0}-\frac{k_{\mathrm{mp}}}{1+{k}_{\mathrm{N}}\left[\mathrm{Nutlin}\right]}\left[\mathrm{p}53\right]\left[\mathrm{Mdm}2\right]-{\gamma}_{\mathrm{p}}\left[\mathrm{p}53\right]+{k}_{\mathrm{p}\mathrm{f}}^{\mathrm{p}}\left[\mathrm{PF}\right]\left[\mathrm{p}53\right]\ \left(\mathrm{Type}\ 1\right)$$
(4)
$$\frac{d\left[\mathrm{Mdm}2\right]}{dt}={k}_{\mathrm{m}0}+\frac{k_{\mathrm{p}\mathrm{m}}{\left[\mathrm{p}53\right]}_{t-{\tau}_{\mathrm{m}}}^4\ }{K_{\mathrm{p}\mathrm{m}}^4+{\left[\mathrm{p}53\right]}_{t-{\tau}_{\mathrm{m}}}^4}-{\gamma}_{\mathrm{m}}\left[\mathrm{Mdm}2\right]-{k}_{\mathrm{m}\mathrm{f}}^{\mathrm{p}}\left[\mathrm{PF}\right]\left[\mathrm{Mdm}2\right]\kern0.5em \left(\mathrm{Type}\ 2\right)$$
(5)
where kf0 and γf are the rate of basal production and degradation of the positive feedback gene, PF. The rate constant kf, Michaelis parameter Kf, and time delay τf describe the transcriptional activation of PF by p53. \({k}_{\mathrm{p}\mathrm{f}}^{\mathrm{p}}\) and \({k}_{\mathrm{mf}}^{\mathrm{p}}\) are the rate constant of p53-PF interaction in the Type 1 motif and the Mdm2-PF interaction in the Type 2 motif, respectively.
For both the Type 1 and Type 2 motifs, simulations over a large parameter space returned two distinctive dose-response phenotypes of p53 dynamics. The first phenotype was common between the two motifs and largely similar to the output of the p53-Mdm2 negative feedback alone (Fig. 4B). Therefore, we attributed it to a weak positive feedback effect. The second dynamic phenotype of the p53 dose response from both the Type 1 and Type 2 motifs diverged significantly from the p53-Mdm2 core output, and we thus attributed it to a strong positive feedback effect (Fig. 4C). For the Type 1 motif, the simulated p53 dynamics under strong positive feedback were largely similar to those that we experimentally observed in A549, U-2 OS, and 769-P cells in response to Nutlin-3a. The novel p53 transitional dynamics at intermediate Nutlin-3a concentrations, i.e., an initial p53 pulse followed by an exponential increase of p53 level, were also reproduced. As for the Type 2 motif, it resulted in a different p53 transitional dynamics, in which the initial p53 pulse was followed by a sigmoidal increase of p53 level. This phenotype resembled the p53 response in U-2 OS cells under 5-FU treatment. Interestingly, we found the positive feedback strength was mainly determined by the degradation rate of PF, γf, and the Michaelis parameter, Kf (Fig. 4D and Additional file 1: Figure S3). When either γf or Kf was small under the Type 1 motif, the second dose-response phenotype of p53 dynamics (denoted as the “strong pos. feedback” phenotype) was produced from the model simulation. Under the Type 2 motif, the strong positive feedback phenotype required both γf and Kf to be small. This result makes quantitative sense, as level of the positive feedback gene, PF, increases faster and higher when γf and/or Kf are small, thus resulting in stronger positive feedback effect on p53 induction.
The novel p53 transitional dynamics provide previously unexplored quantitative features to infer p53 pathway motifs and understand their functional impacts. Intuitively, the change of p53 dynamics from pulsing to an exponential or sigmoidal increase is due to the differential feedback contribution in time from the p53-Mdm2 negative feedback and the p53-PF positive feedback. In the early phase of p53 upregulation, the inhibitory effect from Mdm2 dominates, restraining p53 in a low, pulsing mode (Fig. 4E). As Mdm2 level reaches a saturating state, the upregulation of the positive feedback gene, PF, continues. At the turning point, the activating effect from PF outweighs the inhibitory effect of Mdm2, thus causing p53 dynamics to change to a different, high-level induction mode. The correlation analysis of the turning point characteristics, including the time at which the p53 dynamic mode changes and the p53 level at the point of change, with the different rate constants showed that the turning point did not depend on the rate constants associated with PF (data not shown). This further indicated that the turning point is controlled by Mdm2. Specifically, we found the turning point depended most strongly on kmp, the rate constant of Mdm2-mediated p53 degradation, pointing to the inhibitory strength of Mdm2 over p53 as the determinant of the switch of p53 dynamics in time (Fig. 4F). Overall, our simulation analysis revealed a possible dynamic origin of the new p53 transitional dynamics that we observed in response to Nutlin-3a and 5-FU and suggested that the therapeutic effects of these two drugs in some mammalian cell types are mediated by not only inhibiting Mdm2 but also activating additional positive feedback loops of the p53 pathway.
One well-known positive feedback component in the p53 pathway is PTEN, and previous modeling analyses have attributed differential p53 dynamics to PTEN activity [20, 21]. PTEN is a transcriptional target gene of p53 [31], and can functionally constitute a Type 1 positive feedback to p53 by directly binding to p53 and stabilizing it [32]. PTEN can also constitute a Type 2 positive feedback to p53 via its PIP-3 phosphatase activity that inhibits Akt kinase, leading to attenuation of the Akt-mediated Mdm2 phosphorylation and a decrease of p53 binding by Mdm2 [33]. To examine the possible involvement of PTEN as a positive feedback component to modulate p53 dynamics under the Nutlin-3a and/or 5-FU treatment, we first measured and compared the drug-induced PTEN upregulation levels in the five selected cancer cell lines. Western blot analysis showed no drug-induced PTEN upregulation in any of the cell lines (Fig. 4G). Moreover, RNAi knockdown of PTEN in A549 and U-2 OS, the two cell lines that exhibited distinctive transitional p53 dynamics, did not significantly alter the levels of p53 upregulation in response to Nutlin-3a or 5-FU (Fig. 4H) and p53 dynamics measured by single-cell imaging displayed dynamic phenotypes similar to those without PTEN knockdown as shown in Fig. 1. These results suggest that PTEN is not the key positive feedback component responsible for the differential p53 dynamics that we observed.
p53 dynamics conferred by additional negative feedback
Next, we examined the quantitative impact of additional negative feedback motif on top of the central p53-Mdm2 negative feedback loop. Again, we considered two simple scenarios, where a p53 target gene, NF, attenuates p53 upregulation either directly (Type 1) or by activating Mdm2 (Type 2) (Fig. 5A). Mathematical formulation of the additional negative feedback is largely similar to Eqs. (3)–(5), except for changing the signs of the last term in Eqs. (4) and (5) to account for the inhibitory effect of NF on p53 level. As expected, simulations of these two negative feedback motifs under weak p53-NF or Mdm2-NF feedback strength produced the same p53 dynamics as discussed above for the core module of p53-Mdm2 negative feedback alone. Under strong NF-negative feedback strength, both Type 1 and Type 2 motifs produced an extended large pulse as drug concentrations increased, with Type 2 motif resulting in sharper pulsing features (Fig. 5B). This illustrated a general effect of negative feedback in promoting p53 pulsing, retraining overall p53 induction at a low level, which we previously found to promote cell cycle arrest over cell death [15]. Different from the positive feedback motifs, we found the negative feedback strength of the Type 2 motif was determined mainly by the basal production rate of NF, kf0, and the rate constant of Mdm2-NF interaction, \({k}_{\mathrm{mf}}^{\mathrm{n}}\), and both of these rate constants had to be large in order to render a strong negative feedback effect from the Type 2 motif (Fig. 5C and Additional file 1: Figure S3).
The most widely studied negative feedback regulator that downregulates p53 level and activity is the serine/threonine phosphatase, Wip1. Wip1 is transcriptionally activated by p53 in response to various cellular stress stimuli and can directly dephosphorylate p53 at Ser15, thus forming a Type 1 negative feedback motif to attenuate p53 induction [34, 35]. Wip1 can also dephosphorylate Mdm2 at Ser395, which enhances Mdm2 affinity for p53 and the subsequent Mdm2-mediated p53 degradation, thus rendering a Type 2 negative feedback motif [36]. Of the five cancer cell lines that we profiled, MCF7 is evidently the one that strongly depends on the negative feedback regulations of p53 pathway, as it exhibits p53 pulsing similar to phenotypes shown in Fig. 5B in response to all three drugs. In our previous study, we already confirmed Wip1 played a crucial role as a negative regulator to promote p53 pulsing in MCF7 cells upon Etoposide treatment [15]. Therefore, here we only examined the involvement of Wip1 in mediating the p53 pulsing response to Nutlin-3a and 5-FU. Western blot analysis confirmed that MCF7 expressed much higher level of Wip1 than the other four cancer cell lines, and treatment of both Nutlin-3a and 5-FU induced upregulation of Wip1 in MCF7 cells (Fig. 5D). Knockdown of Wip1 by RNAi significantly enhanced p53 upregulation upon Nutlin-3a treatment (Fig. 5E, left panel), and p53 dynamics of nearly 40% MCF7 cells changed from an extend large pulse to monotonic induction (Fig. 5F). Wip1 knockdown also promoted monotonic p53 induction in response to 5-FU, though western blot analysis did not show an evident increase of the ensemble p53 induction level (Fig. 5E, right panel). This could be due to the fact that 50 μM 5-FU activated an extended large pulse of p53 in only 30% MCF7 cells, and change of p53 dynamics in about 50% of these MCF7 cells to monotonic induction by Wip1 knockdown (Fig. 5F) may not result in a large enough change in ensemble p53 level that is measurable by western blot. Overall, our results pointed to Wip1 as the key negative feedback component that promotes p53 pulsing in response to all three anticancer drugs.
In addition to the strong negative feedback phenotypes as discussed above, we found the presence of a weak negative feedback could be a possible mechanism underlying the bimodal switch of p53 dynamics that we observed for Etoposide. Simulation of the DNA damage response module (Fig. 5G), i.e., ATM/p53/Mdm2/Wip1, under weak Wip1-negative feedback strength showed a p53 dose response with a more distinct separation of the dynamic mode of p53 pulsing and monotonic induction. As shown in Fig. 5H, the central ATM/p53/Mdm2 motif without Wip1 generated p53 transitional dynamics in the form of an initial pulse followed by an elevated plateau. The presence of additional Wip1-negative feedback enhanced the pulsing characteristics at intermediate Etoposide concentrations, leading to a much lower steady-state plateau of p53 level. Given the optical and cellular noises in the experimental data, features of the p53 transitional dynamics may be further attenuated. Therefore, effects from additional weak negative feedbacks in the p53 pathway, such as via low expression of Wip1, may account for the bimodal p53 dynamics that we experimentally observed for A549, U-2 OS, and A375 in their Etoposide response, i.e., the cell population shifted from p53 pulsing directly to monotonic induction without an observable p53 transitional dynamics.
In all simulation analysis described above, we set the time delay for the additional positive and negative feedback gene to be the same as that for Mdm2, i.e., τf = 2.1 h. In general, we found decreasing the time delay τf in the positive feedback loops accelerated the switching of p53 dynamics from pulsing to exponential/sigmoidal increase, while increasing the time delay (i.e., slowing down PF upregulation) delayed and attenuated the transition. As for the negative feedbacks, shorter delay time further enhanced the suppressive effects of the negative feedback in attenuating both the p53 pulsing amplitude and the steady-state plateau level, e.g., similar to features experimentally observed in MCF7 cells (Fig. 5I, τwip1 = 1 h). A longer delay time prolonged the pulsing period and increased the pulsing amplitude, in particular for the first pulse and at high drug concentrations, leading to a more bimodal separation of the p53 dynamic modes of periodic pulsing and an extended large pulse, which is similar to what we observed in 769-P cells under Etoposide treatment (Fig. 5I, τwip1 = 10 h).