Mathematical modeling of the synergy between hyperthermia and radiotherapy in tumor treatment based on p53 signaling network

The aim of the current study was to investigate the synergistic effect between temperature and irradiation on p53 dynamics using mathematical model in p53 signaling pathway.Delayed differential equations were used to construct the dynamic p53 model. The accelerated τ-leap stochastic simulation algorithm was used to analyze the stochastic behavior.Loewe and Bliss combination indexes were used to calculate the synergy. Numerical simulations were performed in MATLAB software. Results showed that at relatively lower temperatures, the amplitude and characteristic pitch of p53 pulses varied with changing temperatures.The amplitude and duration of p53 pulses were highly variable. At temperatures below 39 °C, the amplitude of the first p53 pulse was increased when temperature was elevated, whereas the characteristic pitch of p53 pulses was decreased with increasing temperature.Under mild hyperthermia (≥ 41 °C), p53 pulses were disrupted and p53 proteins became steadily accumulated.The patterns of periodicity in auto-correlation plot gradually vanished when the temperature was increased. With the metrics of cumulative and maximal p53 levels, there existed notable synergistic effects between the temperature and irradiation doses. In addition, the effect of temperature on p53 dynamics was reversible.To sum up, temperature could significantly affect dynamic p53 patterns.Radiotherapy may also benefit from hyperthermia in tumor treatment.