The kinase inhibitor Wortmannin (Wm) was used in previous works [7, 62] to study the effects of transient activation of the p53 network. Wortmannin is a broad-range kinase inhibitor effectively abrogating the activities of many kinases, notably the upstream kinases ATM and DNA-PK. In these studies, Wm was added shortly after the cells were damaged and single cell pulse analysis was performed. The authors found a reduced number of pulsing cells dependent on the time point of Wm addition and stated an all-or-none response with respect to amplitude and widths of the p53 pulses. Consequentially it were these studies, which first introduced the concept of excitability to explain the p53 dynamics in response to DSBs.
However, by disabling ATM the p53 network considered here it the model looses its only positive feedback. The theoretical considerations undertaken in section 1.3 therefore render an excitable behavior of the model downstream of ATM as impossible, given that there is no other positive feedback on p53.
Moreover, simulations show a graded dependence of pulse amplitude and width on the time point of Wm addition, results are shown in figure 1.44. By lowering the amount of active ATM within a pulse formation process, Mdm2 levels can recover sooner and P53 is set back to the steady state concentration before a full pulse can evolve. To address the question if the model maybe still lacks a prominent feedback mechanism, the raw data used in ref. [62] shall be reanalysed.
In these experiments, the cells were damaged with a high dosage of NCS and subsequently imaged for six hours. Wm was added at different time points for each condition and thereafter refreshed to continuously inactivate the upstream kinases.
An important part of pulse detection for the p53 data involves a threshold for the minimum amplitude a pulse should have to be identified as such. Also the wavelet based method used for the analysis here can be deluded by some random fluorescence signal variations. The fraction of responding cells, the are ones who show a pulse, as a function of the amplitude threshold is shown in figure 1.45.
As expected the number of detected pulses decreases with increasing amplitude threshold. The question about the right threshold is hard to answer exactly.
Therefore the subsequent analysis will be done for three representative threshold values. In the results of ref. [62] a response rate of around 0.6 is reported for the control condition. This suggests, that a very high threshold was chosen in their analysis.
To make the effects of Wm on the pulse amplitudes for different thresholds and also to the results of the model comparable, the pulse amplitude of the control condition is set to one. With this, the amplitudes of the conditions with inhibitor addition are given as the ratio of the amplitude of the unperturbed p53 system.
In figure 1.46 the results of the data analysis for three different thresholds and the model output are shown. The earlier the inhibitor is added the lower are the p53 pulse amplitudes to be observed. This effect gets smaller with higher thresholds for the pulse detection, as this effectively filters out the smaller pulses.
In this sense, with higher thresholds the analysis here converges to the results of ref. [62]. As already seen in figure 1.44 the model qualitatively shows exactly
Figure 1.44.: Deterministic simulations of the inhibitor experiments. Dashed lines correspond to Wortmannin addition after 60 minutes, point-dashed lines after 15 minutes, of stimulation. The system was started above the excitation threshold. Upon the indicated time points, a strong degradation term mimicking the effects of Wm was switched on in the r.h.s. of the ATM equation of the p53 model. The model predicts lower pulse amplitudes and smaller widths compared to the control condition.
this behavior, although the effect is more pronounced. Reasons for that might be that there are some intermediate and redundant kinase species acting on the P53-Mdm2 core negative feedback which are not covered by this minimal p53 model. These may longer suppress the P53 antagonist Mdm2 and therefore buffer the sudden absence of active ATM in time, effectively adding inertness to the systems dynamics. Additionally, the kinetics of the kinase inhibition by Wm are unknown. In the model, as can be seen in figure 1.44, its inhibiting action kicks in instantly after addition. Lowering this rate of inhibition would trivially lead to bigger p53 pulses in the model. The same analysis for the pulse widths yields comparable results. However, given the low time resolution in this data set of only 25 time points for the whole observational period, this analysis has more uncertainties and is therefore omitted here, As a last remark it should be stated here, that the analysis was supported by visual inspection of single trajectories to double check that detected low amplitude pulses are indeed present in the data and not artefacts of the detection algorithm.
The observation of figure 1.45, that the addition of the kinase inhibitor Wm lowers the response rate of a stimulated cell population in a time dependent manner is not captured by the model simulations. This can be understood by noting, that the timing of the first pulse is very heterogeneous within a cell population. This is shown in figure 1.47, where the distribution of the peak times is shown. It is striking that the timing of the detected pulses is shifted
Figure 1.45.: The fraction of cells to be identified as responding as a function of the amplitude threshold used for the pulse detection. The addition of the inhibitor Wm generally decreases the number of cells showing a pulse. The earlier Wm is added, the more cells show no p53 pulse at all. A comparison to the results reported in ref. [62] show, that a very high threshold was used in their analysis.
towards earlier time points the earlier Wm is added. It is evident that the initiations of the individual pulse formations shift accordingly. But this means that compared to the control condition, the potentially later forming pulses are much stronger inhibited or completely abrogated by the kinase inhibitor. These are surely contributing to the lower response rates. As the cell state is modeled completely homogeneous there is no cell-to-cell variability present in the model to account for the observed different pulse timings. This explains at least in part that the lower population response rates upon Wm addition can not be captured by simulations so far.
In this section the predictions of the model led to a careful reanalysis of published data. In accordance with the simulations, the inhibitor Wm indeed has an influence on the pulse amplitude. This is a strong check for model consistency. If the reanalysis would not have shown such effects, the assumed underlying regulatory network would have been rendered incomplete, as this would be a strong evidence for another upstream kinase independent positive feedback present in the system to predominantly account for the excitability.
Therefore, these results assure, that the positive feedback employed in the model is indeed important for the excitable pulse formation.
Figure 1.46.: Comparison of median amplitudes extracted from the data for different time points of Wm addition with model predictions for different detection thresholds. The earlier the inhibitor Wm is added, the lower are the resulting p53 pulses. This effect gets smaller with higher thresholds. The model qualitatively reflects this behavior, although the effect of the inhibitor is more pronounced in the simulations.
Figure 1.47.: Distribution of the p53 pulse peak timing for strongly stimulated cells. The kinase inhibitor Wm is added as indicated in the legend.
The earlier it is added, the more of the detected pulse peak times are shifted towards earlier time points. Cells in which the pulse formation started later will not develop a pulse depending on the time point of Wm addition. This explains at least in part the lower response rates observed in figure 1.45.