Dynamics of the p53 response to ionizing and ultraviolet radiation

The tumor suppressor protein p53 compiles information about cellular stressors to make decisions on whether the cell should survive or undergo apoptosis. However, the p53 response depends on the source of damage, displaying a ‘digital’ oscillatory response after ionizing radiation (IR) damage and a proportional non-oscillatory response following UV damage. We propose a mathematical model that qualitatively replicates this observed behavior. The difference in p53 dynamics in the model results from two mechanisms: IR damage is fully detected minutes after exposure while UV damage is detected over several hours; and the p53-controlled transcriptional response is dominated by inactive p53 following UV damage. In particular, we hypothesize that an unidentified positive feedback loop controlled by inactive p53 is required to maintain the qualitative high p53 response to UV damage. This work proposes an explanation for two distinct responses of p53 to DNA damage and how each response can lead to cell cycle arrest or apoptosis. Author summary We propose a mathematical model hypothesizing how the tumor suppressor protein p53 produces two contrasting dynamical responses in response to different types of DNA damage. In particular, we predict the existence of a positive feedback loop controlled by the inactive form of p53, which allows the cell to respond to slowly detected damage. The existence of differing dynamic responses by p53 has implications for our understanding of tumor development and possibly p53-related therapeutic strategies.

Although the functional purpose of p53 within a cell has been widely studied, its 2 dynamics have yet to be fully characterized. The p53 tumor suppressor protein, 3 mutated in 50% of all cancers, is responsible for activating cell cycle arrest or apoptosis 4 programs following cellular stress [1][2][3][4]. To guide these decisions, p53 must integrate 5 information about stress from multiple sources-including DNA damage, hypoxia, 6 transcriptional stress, and telomere erosion-that each affect its total level and 7 activation dynamics differently. It is unknown how p53 controls cell cycle arrest and 8 apoptosis through these dynamical changes. 9 Particularly interesting early work demonstrated that oscillations in total p53 level 10 with a consistent period and amplitude were observed in MCF7 cells exposed to 11 γ-radiation, inspiring a generation of dynamical p53 models [5]. When the same types 12 of cells were exposed to UV light, however, no such oscillations were observed; total p53 13 instead increased proportional to the amount of induced damage [6]. Both phenomena 14 have also been observed in non-cancerous cells [7,8]. Researchers have characterized the 15 first response as digital, and the second as proportional [6]. In this work, we use 16 mathematical models to explore what causes this difference in behavior, and further 17 hypothesize why this change in dynamics is necessary for the p53-mediated apoptotic 18 pathway to function after exposure to each type of damage. 19 Several critical proteins act upstream and downstream of p53 in the apoptotic 20 pathway. We focus on the pathways responsible for detecting double-strand DNA 21 breaks (DSBs) induced by many types of ionizing radiation (IR), and aberrations in 22 DNA structure caused by UV radiation, collectively known as UV photoproducts [9]. 23 DSBs are detected by an aggregate of Mre11, Rad50 and Nbs1 (known as the MRN 24 complex) minutes after damage [10,11]. Of the UV photoproducts, about 85% are 25 cyclobutane pyrimidine dimers (CPDs), and about 15% are 6-4 photoproducts (6-4PPs) 26 [12,13]. 6-4PPs and CPDs on the transcribed strand of DNA are both detected and 27 repaired quickly, while CPDs on the non-transcribed strand remain unrepaired after 28 several hours [14][15][16]. Undetected photoproducts can cause additional DSBs or 29 single-strand DNA breaks (SSBs) when the DNA transcription machinery attempts to 30 process a damaged strand [12]. 31 Both types of damage are detected by cellular pathways that communicate with p53 32 through phosphorylation of ataxia telangectasia mutated (ATM) and ataxia 33 telangectasia mutated related (ATR) proteins [15]. A 2004 study suggests UV-mediated 34 activation of ATR only happens after replication stress, but does not address ATM, and 35 a more recent study shows ATM being upregulated 4-8 hours after UV exposure by 36 DSB formation [17,18]. These two kinases can phosphorylate p53 on Ser15 (a state 37 which we call p53-arrester), modifying its transcriptional activity; and phosphorylate 38 Mdm2, the primary regulator of p53, on Ser394, targeting it for 39 autoubiquitylation [6,19]. This downregulation of Mdm2 allows cellular p53 levels to 40 rise, promoting transcription of p53 binding targets. We give special attention to two 41 transcriptional targets: PTEN, which sets off a cascade sequestering Mdm2 in the 42 cytoplasm through suppression of Akt; and Wip1, a phosphatase which acts to 43 deactivate members of the p53 apoptotic pathway once damage is repaired [20][21][22].

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Wip1 has been shown to dephosphorylate both ATM p and ATR p [23]. 45 Mathematical models of p53 damage response have considered the IR and UV 46 damage responses of p53 separately, using the fact that p53 does not oscillate in 47 response to UV damage to simplify dynamics, or accounted for the difference by 48 assuming Wip1 and ATR p do not interact [6,24]. Previous work has centered around 49 p53-Mdm2 oscillation, attributing it to Mdm2 overregulation, Wip1-ATM p 50 downregulation, spatial dynamics or stochasticity [25][26][27][28][29]. This paper instead asks how 51 and why p53 levels rise proportionally to UV damage level while oscillating after IR

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By creating a system which can replicate the p53 response to both types of damage, 54 we develop several new predictions about how the p53 pathway works. We first propose 55 that the difference in downstream damage response to UV and γ-radiation damage 56 arises because the p53 pathway responds quickly to IR damage, but slowly to UV 57 damage. Furthermore, in order to properly respond to UV damage, we predict the 58 existence of a stabilizing feedback loop released by inactive p53 and suppressed by 59 active p53. These predictions suggest the oscillatory and non-oscillatory responses may 60 aid the cell in responding to both slowly and quickly detected DNA damage.

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CPDs on the transcribed strand are detected (k ctd ) and repaired (k ctr ) quickly.

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CPDs on the non-transcribed strand are detected slowly (δk ctd , δ < 1), and can become 84 DSBs if they are not repaired before the DNA strand is split by replication 85 machinery [16].The cell is assumed to be in S phase for the duration of the simulation. 86 Here, we assume the speed of nucleotide excision repair (NER) and DNA replication is 87 limited by the amount of available DNA polymerase in the cell [38]. because it is carried out by phosphatases such as Wip1.

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Downstream of ATM p , we consider p53 and its transcriptional targets. p53 exists in the model in two classes: unmodified (p53) and Ser15-phosphorylated (p53 a ). Nucleic p53 upregulates transcriptional targets by binding in tetrameric form to their promoter regions [39]. Since p53 dimerizes cotranslationally, concentrations of p53 are understood to be concentrations of p53 dimers, where tetramers are dimers of dimers [39]. Binding to promoter regions therefore occurs at a rate proportional to [p53] 2 , [p53 a ] 2 , or both. Tetramers of p53 and p53 a are ignored in this work. In accordance with experimentally observed p53 behavior, unmodified p53 is produced at a high, constant rate, then quickly ubiquitylated by nucleic Mdm2, after which it is degraded or shuttled to the cytosol. Mdm2, the primary regulator of p53, is split into three classes: cytosolic Mdm2 (Mdm2 c ), nucleic Mdm2 (Mdm2 n ), and Ser394-phosphorylated nucleic Mdm2 (Mdm2 np ). Mdm2 is assumed to be quickly shuttled to the cytosol once produced. To model p53 upregulation of Mdm2 without tracking Mdm2 mRNA, we let P be the probability that p53 is bound to the promoter region of Mdm2, k on1 be the rate of binding of a single inactive p53 dimer to the Mdm2 promoter region, k on2 the rate of binding of a single active p53 dimer to the same region, and k of f be the dissociation rate of tetramers from the promoter region. Then If the probability equilibrates quickly, we estimate This term is scaled in the full model by combined transcription/translation rate k tm , 110 with kon2 kon1 = k sm and Once sequestered in the cytosol, Mdm2 cannot affect nucleic p53 levels until 112 phosphorylated on Ser186 by Akt p , promoting its transfer to the nucleus. Nucleic

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Mdm2 is responsible for downregulating nucleic p53, but can also be phosphorylated on 114 Ser394 by ATM p , targeting it for autoubiquitylation and subsequent degradation.

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Phosphorylated Mdm2 can be rescued from its fate by spontaneous dephosphorylation 116 or by Wip1 interference.

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The other transcriptional targets of p53, PTEN and Wip1, are upregulated by p53 in 118 a rate-limited manner proportional to p53 2 or p53 2 a , respectively. Two other 119 components of the Akt/PTEN pathway are included in the system: PIP 3 , which can be 120 formed from PIP 2 at a substrate-limited rate and dephosphorylated by PTEN, and 121 Akt p , which is activated by PIP 3 [40]. Wip1 is capable of dephosphorylating ATM p ,

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Mdm2 np , and p53 a , helping return the system to a pre-damage state. 123 We assume no change in total ATM, PIP2, or Akt concentration, and nondimensionalize the total available amount of each protein to 1, such that the conservation equations account for the active and inactive states of each protein. We also assume PTEN 124 equilibrates quickly once its transcriptional switch is flipped by an increase in p53 125 concentration, and normalize by the ratio of transcription rate to decay rate, such that 126 PTEN is represented in the full model by The three conservation equations, along with this system of differential equations, 128 form the transcriptional response module: .  Fig. 1f of [6]. For the IR response, we minimized the sum of the least squares distances 143 from the model period, amplitude, and mean to the respective average period, 144 amplitude and mean of Fig. 1C in [6]. Fibroblast data suggest that CPDs are initially repaired quickly, but that after the 150 percentage of CPDs remaining in the cell after 8 hours is much higher than we would 151 predict from an exponential model with a constant repair rate [30]. Furthermore, in 152 MCF7 cells, the post-UV p53 response is delayed by 30 minutes to 5 hours [6]. Both sets 153 of data suggest that not all UV damage is treated equally: some portion of damage is 154 detected and repaired quickly without upregulating the p53 pathway, and some damage 155 evades initial detection and repair but upregulates the p53 pathway. If we assume 156 quickly detected CPDs can upregulate p53 through ATR p , it is impossible to induce the 157 observed delay in p53 induction. Conversely, if we assume all CPDs are detected slowly, 158 p53 upregulation can be delayed-but only in response to a delay in CPD detection, 159 which conflicts with experimental observations. Hence we develop a damage detection 160 model which considers at least two classes of CPDs: transcribed strand CPDs, which 161 are detected and repaired quickly; and non-transcribed strand CPDs, which are 162 detected and repaired slowly [16,31]. Assuming ATR p and ATM p equally upregulate 163 the p53 pathway removes the benefit of this construction, as the ATR-dependent 164 mechanism still receives the largest signal before the observed peak of p53 activity. 165 We resolve the above issues by assuming that photoproducts induced by UV damage 166 are distributed evenly between transcribed and non-transcribed strands, and that ATM 167 interaction with DSBs dominates ATR interaction with CPDs in p53 activation. We average IR spike [6,7]. Because this is impossible to achieve if Mdm2 overactivity causes 194 oscillations whenever p53 crosses a threshold, we hypothesize that additional p53 195 targets must be involved in creating the two distinct dynamical responses.

Michaelis
196 Figure 2. A demonstration of the failure of the simple model, which ignores the downstream transcriptional targets of the p53 pathway, to properly capture post-UV dynamical response. Oscillations in this system are caused by Mdm2 overactivity (A), but this same mechanism over-suppresses total p53 concentration when the system is exposed to a slowly detected signal (B  [22,34].

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To differentiate the transcriptional responses to slowly and quickly detected damage, 205 we use ATM p as a bifurcation parameter rather than as a state variable. For very low 206 concentrations of ATM p , we do not expect the p53 pathway to be significantly 207 upregulated. However, if ATM p levels rise due to a slowly detected source of damage, 208 we expect ATM p to pass some threshold at which the p53 response is turned on. If the 209 source of damage is quickly detected, we expect ATM p to rise to high levels almost showing the slow-damage transcriptional response in between.

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Mediating the bifurcation profile of the transcriptional module ( Figure 3) allows the 216 creation of a regime in which p53 releases to high levels in response to UV damage, but 217 oscillates in response to IR (Figure 4). Here, the equilibria can be split into three  p53 a (B). Uses best-fit parameters to [6], k pmc = 32 and k dm = 0.1 (where k pmc is the rate of nucleic import of Mdm2 and k dm the basal decay rate of Mdm2). This structure takes on topologically diverse forms depending on the values of the parameters: in C, we set k pmc = 34, connecting the two low equilibrium branches and collapsing the high equilibrium; and in D, we set k dm = 0.0009. A Hopf bifurcation occurs on the low equilibrium branch, decoupling the low equilibrium destabilization from the limit points.
A system with no induced DNA damage stays at low equilibrium levels of p53. The 222 low p53 equilibrium collapses at medium levels of ATM p by a novel codimension-2 223 bifurcation, such that the p53 concentration tends towards high equilibrium in this 224 intermediate region ( Figure 3A). When ATM is activated slowly, as in the case of UV 225 exposure, p53 stays on the low branch until [ATM p ] ≈ 0.6, upon which it is drawn 226 towards the high branch until all damage is repaired. We expect p53 a concentrations to 227 be roughly proportional to the concentration of active ATM p ; however, once the system 228 stabilizes to high p53 equilibrium, increased levels of substrate (p53) compensate for 229 lower levels of activating enzyme (ATM p ). Active p53 is therefore present in higher  However, when damage is detected quickly, ATM p rises to a region where the low 233 equilibrium is stable before p53 levels can escape to high equilibrium. Furthermore, 234 high concentrations of ATM p effectively convert p53 to p53 a , which in turn releases 235 Wip1. In the full system, Wip1 would then interact with ATM p to induce oscillations 236 on p53 level corresponding to a back-and-forth motion on the right branch of the low 237 equilibrium. This mechanism is notably robust when the damage detection module is 238 changed. Since the only requirement on the input is the experimentally observed 239 conclusion that IR-induced damage is detected quickly and UV-induced damage is 240 detected slowly, we observe the same differential dynamic profile in models accounting 241 separately for ATM p and ATR p ( Figure S4). 242 We make additional assumptions about active p53 behavior to guarantee existence of 243 this behavioral regime. For the PTEN pathway to stabilize at medium levels of  • Having two dynamic regimes prevents the cell from overreacting to quickly detected damage, or from underreacting to slowly detected damage • Total p53 levels post-UV damage can be higher than total p53 levels post-IR • By upregulating different proteins, inactive p53 can self-stabilize, but active p53 self-regulates • A positive feedback loop stabilizes inactive p53 of DSB repair rate (k dsbrep ). Since DSBs in the UV damage case are created by stalled 255 repair machinery, they are expected to be repaired significantly faster (k dsbrep = 0.0087) 256 than DSBs created by γ irradiation (k dsbrep = 0.004). Figure 4. Model predictions compared to data from [6]. A Response to γ-irradiation normalized to equilibrium, [DSB] 0 = 5. Of the three illustrative cases provided, the average period was 3.548 hours and the average amplitude was 2.395; here, the model converges to a solution with a period of 2.97 hours and amplitude 1.424. Changing the initial DSB concentration by a factor of 2 did not impact the period or magnitude of oscillations. B Normalized response to UV radiation, demonstrating the proportional post-UV p53 response (combined LS error = 28.75). DSB damage repair (k dsbrep ) is enhanced, as DSBs created during this process stall replication machinery and thus localization for repair would be faster.

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Mechanistic implications 259 This model introduces a robust mechanism that causes p53 to oscillate in response to 260 ionizing radiation and respond proportionally to UV damage.

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The difference in behavior is caused, in part, by a difference in upstream signal 262 strength. Damage caused by ionizing radiation is detected within minutes: this leads to 263 the stabilization of active p53, which upregulates Wip1, which in turn deactivates ATM p , 264 producing oscillations. In contrast, UV photoproducts are detected and repaired over a 265 period of hours, leading to activation of a positive feedback loop that stabilizes inactive 266 p53. The oscillations can be understood as the p53 regulatory network responding to  pathways are only activated if the system spikes multiple times, as has been suggested 280 in earlier works [35]. The oscillations in total p53 level may then be seen as a 281 mechanism for avoiding overreactions to repairable levels of DSBs. In contrast, the 282 cellular response to UV photoproducts depends more on the duration than the  and low levels of kinase. It should also be noted that inactive p53 is capable of acting as 295 a transcription factor, but less is known about its function than active p53 [36].

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The necessity of a slow signaling response, the presence of oscillations, and the 297 ability of a cell to recover after DNA damage is repaired support the paradigm that 298 active p53 is self-regulatory while inactive p53 is self-stimulatory. Not only does active 299 p53 preferentially transcribe regulatory genes such as PPM1D and MDM2, a more 300 subtle form of regulation occurs in which removing inactive p53 also removes its 301 stabilizing effect. Ser15-phosphorylated p53, and suggests nothing about inactive p53 [21]. To address 307 this problem, we plan to conduct experiments on the binding of p53 to the promoter 308 regions of PTEN, Wip1 and Mdm2, and also consider IGF-BP3, which can perform the 309 same role PTEN has in this model [21].

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The bifurcation structure displayed in the transcriptional module is too rich to 311 explore fully in this work. We have successfully derived a simpler model with the same 312 behavior and characterized the unusual codimension 2 and codimension 3 bifurcations. 313 Lastly, the data suggest several improvements which could be made to fully capture 314 the dynamics of p53. Stochastic effects could be incorporated to resolve the changes in 315 p53 oscillation period and amplitude that cannot be explained by this model, and 316 further regulatory mechanisms of p53 must be considered to explain the drop in p53 317 level to below equilibrium post-UV damage [6]. These mechanisms may involve tracking 318 the replication phase of the cell, as the cell in our model is assumed to always be in S 319 phase. We also observe that the MCF7 cells used in experiments in [6] do not 320 necessarily converge to the high equilibrium; this is consistent with the observation that 321 MCF7 cells are deficient in apoptotic response, but measuring the p53 response to UV 322 damage in non-pathological cell lines would help to further elucidate the structure of Mdm2 and Wip1 sufficient to produce the post-damage dip in p53 concentration shown 328 in Fig. 1f of [6]. Continued efforts by our group and others on this model of the 329 dynamic response of p53 activation may lead to a better understanding of p53 function, 330 leading to diagnostic and perhaps one day clinical applications for patients with cancer. 331 CPD detecton and repair module. Since ATR could still be activated by transcribed strand CPDs, it was not possible to reconcile the fast CPD detection and repair rates with the delay in p53 induction shown in [30].
S4 Fig. Images from E.A. Fedak, Dynamics of the p53 response to ultraviolet and ionizing radiation, Poster session presented at SMB Annual Meeting, 2017, Salt Lake City, UT. A In response to normalized ionizing ratdiation damage, total p53 levels oscillate using the earlier ATR p -dependent model. B In response to different levels of UV damage, total p53 level rises proportionally to the amount of damage caused.  Table. Parameters used in the simple model.
S2 Table. Parameters used in the CPD detection module.
S3 Table. Parameters used in the nondimensional full model.

S1
File. An expanded description of models and methods.