Mathematical and computational analysis of intracelluar dynamics 5

Chapter Implications of p53 Oscillations in Cell Survival and Death Studies of global cellular regulatory networks have shown that p53 is a major network hub whose perturbations are expected to affect many biological pathways regulating cell cycle, apoptosis, ageing and development (Royds and Iacopetta, 2006) Thus, the consequences of p53 oscillations may be wide-ranging For example, these oscillations may be correlated with predisposition to cancer (Collister et al., 1998), as suggested by studies with Bloom’s syndrome patients whose abnormal fibroblast cells display p53 oscillations distinct from wild-type cells upon DNA damage; Bloom’s syndrome patients have high tendency for tumorigenesis Even so, biological functions of such oscillations remain elusive This might be attributed to the fact that since p53 is involved in many regulatory feedback loops (Harris and Levine, 2005), any biological role of p53 oscillations is likely to be nonintuitive, which confounds the elucidation of these roles For this particular purpose, mathematical modeling is useful as it can elucidate counter-intuitive systems behaviors arising from complex non-linear interactions To study the roles of p53 oscillations however, mathematical models must encompass relevant pathways that crosstalk with the p53-MDM2 feedback loop One such pathway is the p53-AKT network studied previously, which embeds the p53-MDM2 feedback loop 75 In this chapter, the biological roles and consequences of p53 oscillations on the control between cell survival and death in the context of the p53-AKT network is investigated It will be shown that p53 oscillations markedly decrease the IR intensity threshold level at which switching to a pro-apoptotic state occurs Furthermore, several biological advantages conferred by p53 oscillations are demonstrated, including the increased ability of p53 as a transcription factor to induce expression of pro-apoptotic target genes at higher levels 5.1 Formulation of the kinetic model The genesis of p53 oscillations requires a finite time lag between MDM2 protein expression and p53 degradation, which depends on cumulative time delays from transcriptional, translational and translocation processes of MDM2, as well as kinetics of MDM2-mediated p53 degradation The cumulative delay is estimated as 40 (Ma et al., 2005) This is significantly shorter than the reported 90 to 150 time delay of MDM2 oscillation peaks from p53 peaks (Geva-Zatorsky et al., 2006) Furthermore, given that p53-MDM2 oscillations are observed only upon UV or gamma radiation in specific cell types, the time delay associated with MDM2 expression cannot explain for the presence of such oscillations as p53 transcription of MDM2 is ubiquitous in a majority of cell types upon irradiation (Vogelstein et al., 2000; Momand et al., 2000; Bond et al., 2005; Piette et al., 1997; Momand and Zambetti, 1997; Juven-Gershon and Oren, 1999; Moll and Petrenko, 2003; Iwakuma and Lozano, 2003; Alarcon-Vargas and Ronai, 2002; Horn and Vousden, 2007) For 76 these reasons, cell type and stress specific regulations of the p53-MDM2 feedback loop are likely to play a central role in the genesis of p53-MDM2 oscillations Indeed, irradiation-specific post translational modifications of p53 and MDM2 lead to significant retardation of the kinetics of MDM2-mediated p53 degradation (Section 2.2.2 of Chapter 2), thereby extends the time lag between MDM2 expression and p53 degradation Interestingly, removal of ATM-mediated destabilization of MDM2 upon irradiation eradicates p53-MDM2 oscillations no matter how long the MDM2 expression time delay is set (Ma et al., 2005; Wagner et al., 2005) Section 5.1.1 describes in detail as to how this particular regulatory mechanism is accounted in the model Besides, p53 transcription of PTEN is cell type specific that is essential for p53 to antagonize AKT; p53 transcription of PTEN upon irradiation-induced DNA damage has been reported in cells and tissues where p53 oscillations are observed Notably, positive feedback loops, such as p53-AKT loop studied in this thesis, supplementing the p53-MDM2 negative feedback loop has been proposed to induce p53 oscillations (Section 4.2 of Chapter 4) The mechanisms as described are implemented in the model shown in Figure 5-1 that shall be referred to from hereon as Model M4 It is an extension of Model M1 that is previously studied in Chapter (see Figure 3-1 of Chapter 3), which exhibits bistability and predicts switching behavior between pro-survival and proapoptotic cellular states The extension included in Model M4 involves two additional part lists namely, the mRNA transcripts of the MDM2 and PTEN genes (these transcripts are symbolized by mdm2 and pten, respectively), as depicted in red in Figure 5-1 The inclusion of mdm2 facilitates an implicit consideration of the 77 transcriptional and translational delays of p53-dependent MDM2 expression As explained above, an implicit inclusion of MDM2 expression delay in this context is adequate as it is not a likely reason for p53-MDM2 oscillations In fact, Model M4 combines key features of a relaxation oscillator and a delay oscillator v0 v5 v1 p53 v16 v11 v12 pten v13 PIP2 v2 PIP3 v14 v8 vm16 PTEN v15 AKTa AKT vm8 v6 v4 mdm2 v7 v10 MDM2 v3 vm6 MDM2a v9 Figure 5-1 Kinetic model of the oscillatory p53-AKT network, Model M4 Model M4 is an extension of Model M1 (Figure 3-3 of Chapter 3) in which mRNAs of PTEN and MDM2 genes are included (depicted in red) The vr’s are the rate equations of each reaction step Broken edges denote enzymatic reactions whereas full edges denote mass action reactions All part lists are at the protein level except for those depicted in red AKTa and MDM2a denote biochemically active AKT and MDM2 proteins upon phosphorylation In the model, p53 is transcriptionally-active where it transcribes target genes, MDM2 and PTEN The ODEs, rate expressions and the associated kinetic parameters values of Model M4 are given in Appendix A-10 Some of the kinetic parameter values, which are associated with rate equations that describe the p53-MDM2 feedback loop, are modified from Model M1 to fit experimental observations in single cells (reviewed in Section 4.1 of Chapter 4) namely, periods of sustained oscillations of p53 and MDM2 78 range from to hours, peaks of MDM2 oscillations lag behind p53 peak for 1.5 to 2.5 hrs and periods of oscillations decrease with increasing IR intensity The modified values are within the order of magnitudes that were obtained from literature surveys as described in Appendix A-2 5.1.1 Simulating the DNA damage signal transduction pathways As p53-MDM2 oscillations are exhibited upon DNA damage, kinetics of the DNA damage signaling to the p53-AKT network has to be considered As reviewed in Section 2.2.2 of Chapter 2, post-translational modifications of p53 and MDM2 upon DNA damage translate to an increase in the kinetic rate parameter for p53 synthesis and activation (k0) as well as the degradation rate parameter of active MDM2 (k9) in Model M4 The trend of these two kinetic parameters as a function of the extent of DNA damage depends chiefly on the kinetics of the DNA damage signal transduction pathways However, as reviewed in Section 2.3 of Chapter 2, several key issues confound the simulation of these pathways First and foremost, current knowledge about the part lists and their interaction mechanisms are still incomplete Despite that, existing network topologies of these pathways are surprisingly complex – besides the many feedback loops, several redundant sub-networks are present (see Figure 2-3 of Chapter 2) Particularly, the relative contribution of each of the sub-networks on the regulation of the kinetic parameters k0 and k9 might be cell type specific, which has not been determined so far As such, both k0 and k9 are assumed to be directly proportional to IR intensity (ρ), i.e., 79 k = k 0,basal + k 0, IR * ρ k = k 9,basal + k 9, IR * ρ (5-1) where k0,basal and k9,basal are basal value of k0 and k9 under no DNA damage; k0,IR and k9,IR are proportional constants (values of k0,basal, k9,basal, k0,IR and k9,IR are given in Appendix A-10) Nonetheless, simulations are repeated for all other biologically plausible variations of k0 and k9 with ρ (see Section 5.9) 5.2 Steady states and oscillations Steady states of Model M4 were determined using the method as described in Section 3.3.1 of Chapter The steady states of p53 and active MDM2 (MDM2a) as functions of ρ (ionizing radiation intensity) are shown in Figure 5-2 80 A [p53ss] 10 p (Gy) ρ (Gy) 15 20 25 10 (Gy) ρp(Gy) 15 20 25 B [MDM2ass] Figure 5-2 Model M4: steady-state bifurcation diagrams of p53 and MDM2a Steady states of (A) p53 and (B) active MDM2 (MDM2a) as a function of ρ (the abscissa) Local stability of these states is indicated as either stable (black curve: stable nodes; dark gray curve: stable spirals) or unstable (broken black curve: saddle nodes; light gray curve: limit cycles) Limit cycle oscillations whose amplitudes are shown by the dots arise from the unstable steady states (light gray curve) in the lower (A) or upper (B) branch of the steady state curves Units of vertical axes are in µM Units of abscissa are in Gy Model M4 also exhibits multiplicity of steady states within a range of ρ (6 to 20.8 Gy – in Figure 5-2) As in Model M1, within this range of ρ, the high-p53 and low-MDM2a (and low-AKTa) pro-apoptotic steady states are all locally stable nodes, and the middle branch of steady states are all unstable saddle points (local stability is determined by the method as described in Appendix A-4) In contrast to Model M1, however, Model M4 exhibits oscillatory dynamics in all the low-p53 and highMDM2a pro-survival steady states due to the inclusion of time-delays via the 81 additional of mdm2; no oscillations are obtained in the pro-apoptotic states (local stability analysis is used to determine steady states exhibiting oscillatory dynamics as described in Appendix A-11) The steady states enveloped by the gray dotted curves in Figure 5-2 exhibit unstable spirals that lead to sustained oscillations or limit cycles The peaks and troughs of these limit cycle oscillations are indicated by the dots above and below the steady states, respectively The remaining pro-survival steady states, which flank the steady states exhibiting limit cycles, exhibit stable spirals that lead to damped oscillations It is interesting to note that the steady state at ρ = Gy is a stable spiral; this result could explain why some cells have been observed to show oscillatory behavior despite the absence of DNA damage (Geva-Zatorsky et al., 2006) The periods of the sustained oscillations in p53, mdm2, MDM2 and MDM2a are identical, which decrease with increasing ρ (Figure 5-3), in accord with experimental observations (Geva-Zatorsky et al., 2006) The model predicts sustained oscillation periods of 3.5 to 5.2 hours that falls within reported experimental values (Geva-Zatorsky et al., 2006) 400 Limit cycle period mdm2 time delay MDM2 time delay MDM2a time delay Time (Min) 300 200 100 0 p ρ (Gy) (Gy) 10 12 14 16 82 Figure 5-3 Model M4: limit cycle oscillation periods and time-delays of mdm2, MDM2 and MDM2a Oscillation properties of p53, mdm2, MDM2 and MDM2a are depicted for the entire range of ρ where the system exhibits limit cycle The gray curve depicts the oscillation periods of p53, mdm2, MDM2 and MDM2a The remaining curves depict the time-delays of the peaks of mdm2, MDM2 and MDM2a pulses relative to the peaks of p53 pulses (see inset) Furthermore, the model reproduces experimentally measured time-delays between the peaks of MDM2a and p53 oscillations (1.2 to 1.9 hours) As expected, both MDM2 and MDM2a have longer time-delay than mdm2 due to transcription and translation processes (Figure 5-3) Generally, these time-delays are not sensitive to ρ On the other hand, the amplitudes of the oscillations in AKTa, PIP3, pten and PTEN are insignificant; i.e., the concentration difference between crest and trough is less than 4% of the mean concentration (data not shown) that could be difficult to detect experimentally 5.3 Cells exposed to increasing IR intensities Computer experiments using Model M4 are performed to simulate the behavior of a cell that is exposed to a pulse of IR with fixed intensity The experiment is repeated as ρ is increased in the range where limit cycle oscillations are exhibited For each simulated experiment, the initial cellular levels of the proteins and transcripts are those of the steady states of a cell unexposed to IR (i.e., the steady state of Model M4 at ρ = Gy) Interestingly, simulations show that the system initially displays a highamplitude oscillation that eventually settles down to the unique limit cycle at each ρ As an example, the time-courses of p53, mdm2, MDM2 and MDM2a are depicted in 83 Figure 5-4 at ρ = Gy in which their first pulse amplitudes are larger than their respective limit cycle Notably, larger initial p53 oscillation amplitudes are also observed in single cells (Geva-Zatorsky et al., 2006) Figure 5-4 Time-courses of Model M4 at ρ = Gy Time-courses of p53 (red), mdm2 (blue, broken line) and MDM2 (blue) and MDM2a (black) are depicted The amplitudes of these initial oscillations are shown in Figure 5-5 superimposed with the steady-state curve of mdm2 This figure shows that the initial amplitudes increase with ρ and, interestingly, that there is a particular ρ = 13.8 Gy (symbolized by ρ*) where the system crosses a boundary surface associated with the unstable steady states (the dotted middle branch of steady states) and gets attracted to the upper branch of stable steady states These steady states correspond to high-p53 pro-apoptotic states Since ρ* is less than the value of ρ corresponding to the rightknee of the steady state curve, ρ* is defined as an early-switching point 84 non-oscillatory p53 is obtained by taking the average levels of the oscillatory p53 crest and trough Figure 5-18 shows that in the presence of p53 oscillations, cells not only require shorter time-to-apoptosis (BCL-2) but also commit to apoptosis at lower ρ This is due to the increased ability of oscillatory p53 to express more BAX protein to antagonize BCL-2 Time-to-apoptosis (BCL-2) (hr) 100 No repair: oscillatory p53 90 No repair: non-oscillatory p53 80 Slow repair: oscillatory p53 Slow repair: non-oscillatory p53 70 60 50 40 30 20 10 ρ (Gy) 10 11 12 13 14 Figure 5-18 Time-to-apoptosis (BCL-2) induced by oscillatory and non-oscillatory p53 The level of non-oscillatory p53 is obtained by taking the average levels of the oscillatory p53 crest and trough at each ρ The difference in the time-to-apoptosis (BCL-2) between oscillatory and non-oscillatory p53 becomes smaller as repair rate is increased (data not shown for moderate repair) 5.6.4 p53 oscillations cannot substantially deplete BCLXL The level of BCL-XL does not fall below the defined apoptotic threshold level when the system is at the pro-survival oscillatory p53 state Instead, as depicted in Figure 5-19, BCL-XL can only be substantially depleted after the early switch to high-p53 state Even so, time-to-apoptosis (BCL-XL) is always significantly longer than time- 103 to-apoptosis (BCL-2) at all ρ and repair rates As kinetic parameter values associated with the reaction steps of BAD/BCL-XL are identical to those of BAX/BCL-2 (Appendix A-12), the longer time-to-apoptosis of BCL-XL is due to AKTa-mediated inhibition of BCL-XL’s antagonist, BAD (Figure 5-15) 10 BCL-2 - no repair Time-to-apoptosis (hr) BCL-XL - no repair BCL-2 - slow repair BCL-XL - slow repair BCL-2 - moderate repair BCL-XL - moderate repair 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 ρ (Gy) Figure 5-19 Time-to-apoptosis of BCL-XL and BCL-2 induced by high-p53 state at various DNA damage repair rates The range of ρ depicted here is after the early-switching point where BCL-XL can be depleted below the defined apoptotic threshold level The time-to-apoptosis of BCL-XL is always longer than that of BCL-2 at all repair rates 5.7 Consequences of p53 oscillations 5.7.1 Sensitize cells to IR-induced apoptosis Two key effects of p53 oscillations are elucidated from the analyses of an oscillatory p53-AKT kinetic model (Model M4) – early switch to high-p53 state and ability to express more amounts of p53-target genes products The consequences of these 104 effects on p53-AKT regulation of the mitochondria apoptotic pathway are subsequently demonstrated using the Apoptotic Model (Section 5.6) In particular, the early switch phenomenon lowers the apoptotic threshold level of ρ at which the system switches to high-p53 state A high-p53 state leads to the fastest time-toapoptosis regardless of DNA damage repair rates (Figure 5-16) This is notable since cell-cell and cell-type differences could result in a range of repair rates and earlyswitching points Moreover, as a high-p53 state is essential to cut off AKT inhibition of pro-apoptotic BAD protein (Figure 5-19), the early switch further entrenches the cell for apoptosis On the other hand, the increased ability of oscillatory p53 to express more pro-apoptotic BAX proteins not only accelerates the time-to-apoptosis appreciably but also commit to cells at lower ρ, as compared to the case of nonoscillatory p53 (Figure 5-18) Taking these results together, p53 oscillations are predicted to sensitize cells towards apoptosis upon IR This prediction can also be interpreted as a decrease in tolerance to IR-induced DNA damage in cells that induce p53 oscillations Several single cell time-lapse microscopy experiments (e.g., Geva-Zatorsky et al., 2006) could be performed to validate key hypotheses generated from the models by taking advantage of the evidence that not every cell (of the same type) would manifest p53-MDM2 oscillations when irradiated with the same IR intensity For instance, only 40% of MCF-7 cells showed oscillations upon 10 Gy of gamma radiation (Geva-Zatorsky et al., 2006) Strictly speaking, a cell could only be in one of the three states: low-p53 (non-oscillatory cells), high-p53 and oscillatory p53 (oscillatory cells) The key prediction that p53 oscillations induce higher level of target gene expression could be tested by semi-quantifying the expression level of a 105 (transfected) luciferase reporter gene that possesses a p53 promoter sequence upon irradiation Oscillatory cells are predicted to express higher intensity of fluorescence than non-oscillatory cells (of the same type); comparisons should be made among cells that expressed similar mean level of p53 Also, an interesting experiment would be to test whether higher p53-dependent expression of cell cycle and DNA repair genes in oscillatory cells could lead to faster cell cycle arrest and repair damage DNA than non-oscillatory cells upon irradiation In contrast, the other key prediction that p53 oscillations lower the IR intensity level at which the system switches to high-p53 state is relatively trickier to perform experimentally It involves the determination of cumulative IR dose that lead to a high-p53 state in each oscillatory and nonoscillatory cells by increasing the IR dose gradually Oscillatory cells are predicted to switch to high-p53 state over a wider range of cumulative IR dose with lower median than non-oscillatory cells Analog and digital forms of p53 oscillations Digital [TP53] 5.7.2 [p53] uM Analog Tim e Figure 5-20 Schematic illustration of analog and digital p53 oscillations Time-courses of analog (blue) and digital (red) p53 oscillations are depicted 106 Analog p53 oscillations display variable oscillation amplitudes at fixed period whereas digital p53 oscillations display variable oscillation periods at fixed amplitude (Figure 5-20) The number of digital p53 pulses has been postulated to act as a time counter for DNA damage repair, after which apoptosis occurs if damage is unrepaired (Lahav et al., 2004) The relevance of digital p53 oscillations in the regulation of apoptosis has also been explored (Zhang et al., 2007) However, digital p53 pulses cannot differentially express target genes for they induce the same amount of gene products for the range of ρ where oscillatory p53 state exists, as the amplitude is constant (Figure 5-14); thus, the time-to-apoptosis is constant Therefore, inducing appropriate amplitude that could response effectively to a wide range of ρ is problematic A slow time-to-apoptosis induced by a small digital p53 amplitude would subject cells sustaining irreparable damage to prolonged exposure to damage that could lead to DNA damage adaptation; whereas a fast time-to-apoptosis induced by a large digital p53 amplitude could result in premature commitment to death In contrast, analog p53 oscillations, which manifest variable amplitudes in response to different ρ, could differentially express target genes (Figures 5-13 and 514B), resulting in differential time-to-apoptosis Plausibility of an analog p53 mode is supported by several reported experimental observations Firstly, p53 oscillation amplitudes show more variability than their periods in single-cell experiments (GevaZatorsky et al., 2006) Secondly, time-to-apoptosis are distinct at low and high ρ At low ρ, induction of apoptosis in normal human fibroblasts occurs on a timescale of days (Suzuki et al., 2005) At high ρ however, substantial apoptosis occurs in mice thymus, spleen, small intestine and colon as early as to hrs post-irradiation that coincides with p53 activation and its associated apoptotic targets (varez et al., 2006; 107 Coates et al., 2003); p53 oscillations have been observed in mice spleen and small intestine (Hamstra et al., 2006) The Apoptotic Model generate analog p53 oscillations when ρ is varied in which predicted time-to-apoptosis by the Apoptotic Model decreases from days to hours as ρ is increased (Figure 5-16) 5.8 Hopf versus homoclinic bifurcation of limit cycles Limit cycles that emerge from a Hopf bifurcation display more variability in its oscillation amplitudes than its periods whereas those that emerged from a homoclinic bifurcation display more variability in its period than its amplitudes (Tyson, 2006) In this aspect, a homoclinic bifurcation produces roughly digital oscillations whereas a Hopf bifurcation produces roughly analog oscillations In addition, although initial response of a system that manifests homoclinic bifurcation is sluggish, it could generate limit cycles with larger amplitudes than a Hopf bifurcation (Tyson, 2006) Manifestation of limit cycles by the two bifurcation types has been illustrated in published p53-MDM2 models (reviewed in Section 4.2 of Chapter 4) Two key experimental observations seem to support for a Hopf bifurcation (Geva-Zatorsky et al., 2006) Firstly, more variability of p53 oscillation amplitudes than their periods is observed Secondly, the initial pulse amplitude of p53 and MDM2a are always larger than their subsequent pulses, indicating that initial response to DNA damage is not sluggish 108 In Model M4, limit cycles emerge from a Hopf bifurcation in which the initial response to DNA damage matches reported experimental observation (Figure 5-4) The comparatively small oscillation amplitudes generated from a Hopf bifurcation is partly compensated by the positive p53-AKT feedback loop Specifically, p53 and MDM2a pulses have larger oscillation amplitudes (higher peaks and lower troughs), longer oscillation periods and longer time-delay of MDM2a peaks to p53 peaks in Model M4 than in a standalone p53-MDM2 model (Figure 5-21) Taken together, the p53-AKT positive loop results in a relatively more defined and distinct pulses over a broader range of ρ These results suggest that the p53-AKT positive feedback loop not only increase the propensity of p53 oscillations but also augments the oscillation A 12 15 18 ρ (Gy) MDM2a oscillation amplitude (uM) TP53 oscillation amplitude (uM) profiles 12 15 18 15 18 ρ (Gy) 150 C 300 Time-delay (min) Oscillation period (min) 400 B 200 100 D 120 90 60 30 0 ρ (Gy) 12 15 18 12 ρ (Gy) Figure 5-21 Limit cycles generated from Model M4 and a p53-MDM2 model The standalone p53-MDM2 model is extracted directly from Model M4 depicted in Figure 51 by considering only reaction steps involving p53, MDM2 and mdm2; kinetic parameters are identical to those used in Model M4 The figures show for the range of ρ where limit cycles exist in Model M4 (black) and the p53-MDM2 model (gray), the respective oscillation 109 amplitudes of (A) p53 and (B) MDM2a, (C) oscillation periods and (D) time-delay of MDM2a peaks to p53 peaks 5.9 Effects of various types of IR response curves The IR response curve describes the rate of change of active p53 synthesis (k0) and the rate of MDM2a degradation (k9) as a function of ρ The assumed linear IR response curve used to simulate Model M4, as defined in Eqn (5-1), shall be referred to as the reference IR response curve and the corresponding generated p53 steadystate curve (Figure 5-2A) is hereon referred to as the reference p53 steady-state curve Because different cell types might manifest different IR response curves, the effects on the p53 steady-state curves are studied using Model M4 5.9.1 Monotonic IR response curves Figure 5-22 tabulates some representative p53 steady-state curves generated from an exhaustive collection of monotonic IR response curves; refer to Appendix A-14 for all possible generated p53 steady-state curves Two particular features of these IR response curves affect the corresponding p53 steady-state curves: Gradient Increasing the slope of an IR response curve lowers the range of ρ where the system exhibits bistability (Figure 5-22A) Moreover, the bistable region contracts that result in a shortened limit cycle range of ρ and consequently, lowers the pro-apoptotic threshold level of ρ Conversely, 110 decreasing the slope of an IR response curve results in a contrary effect (Figure A14-1B) Saturation point An IR response curve that attains and remains at a specific level (saturation point) beyond a particular ρ may be biologically more probable than an ever-increasing one If the saturation point is less than the minimum value of k0 and k9 required to generate bistability, the p53 steadystate curve will have only one pro-survival state manifesting either stable spirals or limit cycles, or both (Figure 5-22B or A14-1D), thus eradicating the high-p53 state However, if the saturation point is less than the value of k0 and k9 needed to generate the right knee of the bistable region, the p53 steady-state curve will have bistable region that extends to infinity (Figure 5-22C or Figures A14-1F and A14-1G) As depicted in Figure 5-22D (or Figures A141I and A14-1I J), only IR response curves whose saturation points are greater than the value of k0 and k9 needed to generate the right knee will produce p53 steady-state curves that are qualitatively similar to the reference p53 steadystate curve [TP53] [p53] A k0, k9 10 ρ (Gy) 20 30 10 ρ (Gy) 20 30 10 30 10 30 C B 20 20 111 E C 10 20 30 10 20 30 10 20 30 10 20 30 H D Figure 5-22 Representative p53 steady-state curves generated from various monotonic IR response curves For each case, IR response curve (black curve) is shown on the left while the corresponding p53 steady-state curve is shown on the right In every plot of IR response curve, the reference IR response curve is shown in gray for reference; the values of k0 and k9 at which they generate the left and right knee of the reference p53 steady-state curve are indicated respectively by the lower and upper horizontal broken lines In every plot of p53 steady-state curve, stable nodes are indicated in black; unstable saddle nodes in red; limit cycles in blue and stable spiral in gray; for reference, the two vertical broken lines demarcate the bistable region of the reference p53 steady-state curve 5.9.2 Bistable IR response curves DNA damage signal transducer ATM, which impinges on k0 and k9, self-activates through auto-phosphorylation in the presence of DSBs (Bakkenist, Kastan, 2003) This classic positive feedback loop has the potential to exhibit bistability, i.e., active ATM could be present at either low or high state This leads to bistable IR response curves in which two possible values of k0 and k9 exist at each ρ in the bistable region Interestingly, bistable IR response curves lead to p53 steady-state curves manifesting more than three steady states (representative cases are depicted in Figure 5-23); refer to Appendix A-14 for all possible generated p53 steady-state curves 112 These p53 steady-state curves can be classified qualitatively into Types I, II and III according to the number and types of steady states manifested Type I curves manifest two oscillatory and one stable node (Figure 5-23A or A14-2A) whereas Type II curves manifest one oscillatory and two stable nodes (Figure 5-23B or A14-2D) Type III curves manifest two oscillatory and two stable nodes (Figure 5-23C) All oscillatory states appear at the low-p53 pro-survival state while all stable nodes appear at the high-p53 pro-apoptotic state The existence of two p53 stable states could be utilized by a cell for transcriptional regulation of specific genes in specific tissues For instance, it has been reported that different threshold levels of ρ are needed for p53 to induce transcription of various pro-apoptotic genes (BAX, FAS, KILLER, NOXA and PUMA) in a same organ, as well as for the same gene in different organs (varez et al., 2006) In contrast, biological role of bi-oscillatory p53 states is unclear As they are adjacent to each other, the system is prone to alternate between the two states that would result in varied p53 oscillation amplitudes, similar to observations reported by Geva-Zatorsky et al., (2006) BA 10 15 10 15 10 15 10 15 C B 113 0 E C 10 15 10 15 Figure 5-23 Representative p53 steady state curves generated from various bistable IR response curves For each case, IR response curve (black curve) is shown on the left while the corresponding p53 steady-state curve is shown on the right In every plot of IR response curve, only the stable lower and upper branch are shown; the values of k0 and k9 at which they generate the left and right knee of the reference p53 steady-state curve are indicated respectively by the lower and upper horizontal broken lines In every plot of p53 steady-state curve, stable nodes are indicated in black; unstable saddle nodes in red; limit cycles in blue and stable spiral in gray (A) Type I: one oscillatory and two stable p53 states (B) Type II: two oscillatory and one stable p53 states (C) Type III: two oscillatory and two stable p53 states 5.10 Effects of total intracellular AKT Using Model M4, steady-state curves of p53 and AKTa as functions of [AKTT] are generated at some representative values of ρ (data not shown); ρ is fixed in each curve As expected, [AKTT] promotes the manifestation of pro-survival steady states, which are limit cycles Oscillation profiles of p53 and MDM2a are next determined for the range of [AKTT] where limit cycle exists at these representative values of ρ Surprisingly, [AKTT] does not influence the oscillation amplitudes (Figures 5-24A and 5-24B) Oscillation periods and time-delay of MDM2a peak to p53 peak however decrease as [AKTT] is increased, but remain relatively constant when [AKTT] > 1.5 µM (Figures 5-24C and 5-24D) Thus, p53 oscillations is digital as [AKTT] is varied but is nevertheless, affected more by ρ than [AKTT] 114 0.8 B A 0.6 0.8 0.4 0.6 0.2 0.4 0.25 0.5 0.75 1.25 [AKTT] (uM) 1.5 1.75 0.2 0.25 0.5 0.75 0.5 1.25 [AKTT] (uM) 0.75 1.5 1.75 1.5 1.75 120 350 D C 110 300 100 90 250 80 200 0.25 0.5 0.75 1.25 [AKTT] (uM) 1.5 1.75 70 0.25 1.25 [AKTT] (uM) Figure 5-24 Oscillation profiles of p53 and MDM2a as functions of [AKTT] at four representative values of ρ Using Model M4, oscillation profiles of p53 and MDM2a are determined for the range of [AKTT] (the abscissas) where limit cycles exist at ρ = Gy (blue), Gy (red), 12 Gy (gray) and 14 Gy (black) Oscillation amplitudes of (A) p53 and (B) MDM2a in which the peaks and troughs are shown respectively as upper and lower curves (C) Oscillation periods of p53 and MDM2a (D) Time-delay of MDM2a peaks to p53 peaks 5.11 Effects of the putative mutual activation loop between p53 and PTEN The implications of the putative p53-PTEN positive feedback loop (refer to Section 2.1 of Chapter for the biological review) on the p53-AKT cellular switch are studied The kinetic model, Model M6, which extends Model M4 (Figure 5-1) by including the p53-PTEN feedback loop, is formulated and analyzed (Appendix A-15) Simulations show that the system is progressively tipped to a pro-apoptotic state at increasing p53-PTEN feedback strength, as MDM2a-mediated degradation of p53 is 115 inhibited under strong feedback strength Furthermore, due to the exceptionally fast rate of PTEN dephosphorylation of PIP3 (direct experimental measurement by McConnachie et al (2003)), a relatively small upregulation of PTEN by the p53PTEN loop is sufficient to inhibit PIP3 and thereby AKT completely 5.12 Summary Simulation of the oscillatory p53-AKT model (Model M4) upon IR-induced DNA damage reproduces sustained p53 oscillation profiles that match single-cell experiments Such oscillations are predicted only at pro-survival steady states Two key effects of p53 oscillations are elucidated First, p53 oscillations markedly decreases the IR intensity threshold level at which switching to a pro-apoptotic state occurs, defined as an early switch This early switch phenomenon is generally conserved in the presence of: variations in the intracellular levels of part lists among cells, cell type-specific differences, and differences in the DNA damage signal transduction kinetics Furthermore, early switching to pro-apoptotic state by random fluctuations of any part list is unlikely The second effect of p53 oscillations is the increased ability as a transcription factor to transcribe higher amounts of target genes as compared to non-oscillatory p53 The consequences of these effects on p53-AKT regulation of the mitochondria apoptotic pathway are demonstrated The most significant role of p53 oscillations is that cells inducing such oscillations commit to apoptosis faster and at lower threshold level of IR Therefore, p53 oscillations are predicted to sensitize cells towards 116 apoptosis upon IR This prediction can also be interpreted as a decrease in tolerance to IR-induced DNA damage in cells that induce p53 oscillations In addition, IRsensitivity seems to be associated with p53 oscillations and the proliferation status of cells In particular, p53 oscillations have so far been observed in proliferating cells both in vivo and in vitro, in which they have been shown to be prone to IR-induced apoptosis as compared to non-proliferating cells In conclusion, the counter-intuitive roles of p53 oscillations in cell survival and death demonstrate the complex systems behaviors that would not be otherwise elucidated from a standalone p53-MDM2 model, or much less, without the aid of mathematical modeling 117 ... (uM) 1 .5 1. 75 0.2 0. 25 0 .5 0. 75 0 .5 1. 25 [AKTT] (uM) 0. 75 1 .5 1. 75 1 .5 1. 75 120 350 D C 110 300 100 90 250 80 200 0. 25 0 .5 0. 75 1. 25 [AKTT] (uM) 1 .5 1. 75 70 0. 25 1. 25 [AKTT] (uM) Figure 5- 24 Oscillation... Analog and digital forms of p53 oscillations Digital [TP53] 5. 7.2 [p53] uM Analog Tim e Figure 5- 20 Schematic illustration of analog and digital p53 oscillations Time-courses of analog (blue) and. .. interval of 0.02 µM For each combination of k0 and j5, a p53 steady-state curve as a function of ρ is computed; k0,basal is set as 0.1 µM/min and j5 is set as 0 .5 µM in the computation of the p53 steady