Oscillations and variability in the p53 system

Abstract

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best‐studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA‐damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low‐frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low‐frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time. ### Synopsis A major challenge of systems biology is to understand the dynamics of regulatory circuits ([Hartwell et al , 1999][1]; [Becskei and Serrano, 2000][2]). In order to understand such circuits, it is important to study them at the level of individual cells, rather than in averages of cell populations (Ferrell and Machleder, 1998). In this study, we investigated the dynamics of one of the most studied protein regulatory circuits in human cells—the p53–Mdm2 negative feedback loop ([Lev Bar‐Or et al , 2000][3]; [Vogelstein et al , 2000][4]; Oren et al , 2002; [Oren, 2003][5]; [Harris and Levine, 2005][6]) in individual living cells. p53 is a tumor suppressor that upregulates a variety of genes that are involved in DNA repair and cell proliferation ([Vogelstein et al , 2000][4]; [Oren, 2003][5]). Interestingly, one of p53's downstream targets is Mdm2, which inhibits p53 activity and targets it for degradation. This negative feedback loop was previously shown, in a study that followed cells over 16 h, to exhibit one to two discrete undamped peaks following DNA‐damaging radiation ([Lahav et al , 2004][7]). Such detailed information is lost in population studies, as the peaks in different cells are averaged together, giving an appearance of damped oscillations. Here we extended our previous study on individual living cells for much longer periods of up to 3 days. In order to trigger the p53–Mdm2 response, we used gamma irradiation that causes double‐stranded DNA breaks. We found that the p53/Mdm2 oscillations are continuous for at least 60 h: many cells show more than 10 oscillation peaks ([Figure 2][8]). We found that the oscillation pattern was highly variable between cells that were genetically identical. In addition to cells that oscillated, other cells showed a dynamic fluctuation of protein levels that did not resemble sustained oscillations. The prolonged experiments indicate that the fraction of cells that show continuous oscillations increases with the irradiation dose: in our previous, shorter experiments, this effect could not be seen owing to the small number of peaks. During the extended duration time‐lapse microscopy of live cells, we observed cell divisions and could address the dynamics of the two daughter cells. We found that sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. We also found that unirradiated cells show slow fluctuations in p53 and Mdm2 levels, with frequencies on the order of 11 h. Finally, we studied several families of mathematical models in order to understand the variability in the dynamics observed in our experiments ([Figure 6][9]). As many of the details of the system are unknown, we studied six different model designs based on known interactions and suggested models of the p53 system ([Tiana et al , 2002][10]; [Tyson et al , 2003][11]; [Ciliberto et al , 2005][12]; [Ma et al , 2005][13]). The main conclusions of the modeling study are as follows: 1. Different models can describe deterministic oscillations, and do so with very similar parameters: ‘consensus parameters’. These parameters, such as p53 and Mdm2 lifetimes, can be directly tested experimentally. 2. We went beyond deterministic models, and performed an analysis of the p53 system with stochasticity in the internal parameters. We find that the best way to get the observed noise in amplitude but relative precision in the period is to add noise to the production rates, rather than degradation rates. This might point to the internal source of the noise in this system. 3. We performed an analysis of internal noise that has slow variation (rather than rapidly varying ‘white noise’ usually employed in most models of biological noise). We find that such slow noise is essential to explain the behavior observed: noise that is too fast or too slow is averaged out and cannot give significant variations in the oscillations. It seems that only noise with frequencies near the resonance frequency of the oscillator can result in the observed amplitude variations. 4. We find that a new checkpoint model captures all of the features of the variability we observe, including low correlation between p53 and Mdm2 peak amplitudes. This model predicts that a factor downstream of p53 inhibits a factor upstream of p53, such as phosphorylated ATM. In summary, this is one of the first studies of a protein circuit as it functions in individual living human cells. We find unexpected...