基于p53信号转导网络数学模型研究热疗联合放疗在肿瘤治疗中的协同效应

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

基于p53信号转导网络数学模型研究温度和辐射在调控p53动力学行为过程中的协同效应。利用时滞微分方程构建p53动力学模型,使用加速τ-leap算法进行随机模拟分析,采用Loewe和Bliss协同指数计算协同性,用MATLAB软件进行数值模拟。结果显示,在较低温下,p53脉冲的振幅和特征基音随温度发生转变。p53脉冲的振幅和周期具有较大的变异性。在39℃以下,p53首个脉冲的振幅随温度升高而增加,而p53的特征基音则随着温度升高而降低。较温和的高温环境(≥41℃)则破坏了p53脉冲,p53蛋白水平呈现持续累积。随着温度的升高,自相关图谱中的周期行为逐渐消失。以p53的累积值和最大值作为评价指标,温度和辐射剂量可产生显著的协同作用。另外,温度对p53动力学的影响是可逆的。总之,温度可显著影响p53的动力学特征。在肿瘤治疗中,热疗亦可为放疗提供有益的帮助。

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 acceleratedτ-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.