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.

Figure 1

Prolonged oscillations in the nuclear levels of fluorescently tagged p53 and Mdm2 in individual MCF7, U280, cells following gamma irradiation. (A) Time-lapse fluorescence images of one cell over 29 h after 5 Gy of gamma irradiation. Nuclear p53-CFP and Mdm2-YFP are imaged in green and red, respectively. Time is indicated in hours. (B) Normalized nuclear fluorescence levels of p53-CFP (green) and Mdm2-YFP (red) following gamma irradiation. Top left: the cell shown in panel A. Other panels: five cells from one field of view, after exposure to 2.5 Gy gamma irradiation.

Figure 2

Nuclear Mdm2-YFP fluorescence in MCF7 cells, U280. (A, B) Oscillations in Mdm2-YFP levels after exposure to 5 Gy (A) and 10 Gy (B) of gamma irradiation. The bottom three panels in (A) and (B) are non-oscillatory cells. (C) Mdm2-YFP dynamics without gamma irradiation. (D) Timing of the nuclear Mdm2-YFP peaks: the horizontal lines show the normalized Mdm2-YFP dynamics over time for 37 cells with ∼5.5-h oscillations. Blue hues indicate low fluorescence levels and yellow-reddish colors indicate high fluorescence levels. Dotted vertical lines are a guide to the eye, indicating 6-h intervals.

Figure 3

Pitch (characteristic period) of Mdm2-YFP signals of cells at various gamma irradiation doses. (A) Histogram of the pitch values from movies of cells exposed to 0, 0.3, 5, and 10 Gy, and from all the movies together. For each movie, the total number of cells is indicated, and the number of oscillating (osc.) cells that had a detectable pitch. (B) Fraction of cells (out of the total number of cells) with a pitch value of 4–7 h, for different gamma doses. Black line is a guide to the eye.

Figure 4

Average amplitude, width, and time delay of oscillation peaks and their variance. (A–C) Average values of the first five p53-CFP (green triangles) and Mdm2-YFP (red squares) oscillation peaks in 146 cells exposed to 5 Gy of gamma irradiation, shown with their standard errors. (A) Average oscillation amplitude of each of the first five peaks (peak to trough). (B) Average width (full-width half-maximum). (C) Average time delay between the p53 peaks and the consecutive Mdm2 peak. (D–F) The distribution of the individual peak amplitude, width, and delay divided by the mean value (note log scale). Black line: Log-normal probability distribution function, with mean=0 and standard deviation=0.22 (D), 0.13 (E), and 0.11 (F). The coefficient of variation (CV) of the original (not log) distribution is indicated.

Figure 5

Dynamics of nuclear Mdm2-YFP fluorescence in sister cells. (A) Mdm2-YFP fluorescence intensity dynamics in cells that undergo division during the movie. Mdm2-YFP fluorescence is shown in black before division, and in blue and green in the two daughter cells. One of the cells in the bottom right panel undergoes a second division, and the second-generation cells are shown in cyan and purple. The top three panels show cells exposed to 0.3 Gy of gamma irradiation (at time zero), and the bottom three panels show cells exposed to 5 Gy of gamma irradiation. (B) Average correlation between 112 sister-cell pairs (normalized mean difference in rank, see Materials and methods) as a function of time following division. Red line: exponential fit, C=2^−t/τ, with τ=11 h.

Figure 6

Models of the p53–Mdm2 feedback loop. (A) The six families of models (see text and Table I). (B) The deterministic or ‘noise-free' dynamics obtained by the models, using parameters and initial conditions in Table II, with ξ(t)=1. Panels are ordered as in part A. (C–E) Examples of the dynamics obtained by these models with noise in protein production rates, ξ(t). The noise ξ(t), which was used for each run, was identical for all models, and is shown for each run in the top panels. The noise was generated as a Gaussian wave-packet with random phases (Supplementary Figure S7), with periods centered around 1 h (C), 12.5 h (D), and 50 h (E), with mean (log[ξ(t)])=0, STD(log[ξ(t)])=0.4, and STD(ξ(t))≈0.5. (F) Averaged relative difference between amplitudes of consecutive peaks (Δh/〈h〉) in simulations of model VI, as a function of noise period.