Elucidating the digital control mechanism for DNA damage repair with the p53-Mdm2 system: single cell data analysis and ensemble modelling.

Recent experimental evidence about DNA damage response using the p53-Mdm2 system has raised some fundamental questions about the control mechanism employed. In response to DNA damage, an ensemble of cells shows a damped oscillation in p53 expression whose amplitude increases with increased DNA damage--consistent with 'analogue' control. Recent experimental results, however, show that the single cell response is a series of discrete pulses in p53; and with increase in DNA damage, neither the height nor the duration of the pulses change, but the mean number of pulses increase--consistent with 'digital' control. Here we present a system engineering model that uses published data to elucidate this mechanism and resolve the dilemma of how digital behaviour at the single cell level can manifest as analogue ensemble behaviour. First, we develop a dynamic model of the p53-Mdm2 system that produces non-oscillatory responses to a stress signal. Second, we develop a probability model of the distribution of pulses in a cell population, and combine the two with the simplest digital control algorithm to show how oscillatory responses whose amplitudes grow with DNA damage can arise from single cell behaviour in which each single pulse response is independent of the extent of DNA damage. A stochastic simulation of the hypothesized control mechanism reproduces experimental observations remarkably well.