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基于果蝇周期蛋白PER调控网络构建的两导数Runge-Kutta算法

DOI: 10.7685/j.issn.1000-2030.2014.03.023, PP. 152-158

Keywords: 果蝇周期蛋白,两导数Runge-Kutta算法,精度,效率

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Abstract:

为更准确地模拟基因调控网络的动力学行为,考虑采用新的两导数Runge-Kutta模拟算法。这种数值算法的特点是在格式中融入了真实解的二阶结构,使得模拟结果更为精确。与通用的经典四级四阶Runge-Kutta算法RK4相比,二级四阶两导数Runge-Kutta算法TDRK2s4具有3个优势1)构造简单,易于编程实现;2)计算成本小,RK4每步需要计算4次非线性函数,而TDRK2s4只需要计算3次;3)存储空间小,RK4方法需要4个内级存储单元,而TDRK2s4只要2个。TDRK2s4用于模拟具有持续振荡特征的果蝇周期蛋白PER与permRNA负反馈调控网络。与RK4相比较,对不同步长(h=1/2,1/4,1/8,1/16),TDRK2s4的误差远小于RK4的误差;而且TDRK2s4对大步长(h=1/2)的误差远小于RK4对小步长(h=1/16)的误差。对固定步长(h=1/4),随着模拟区间的延长,TDRK2s4的累积误差增长十分缓慢,而RK4的累积误差增长很快。对不同步长(h=1/2,1/4,1/8,1/16),TDRK2s4计算耗费的CPU时间也明显少于RK4。TDRK2s4的模拟效率远高于RK4。结论当基因调控网络微分方程组右端函数的导数容易得到时,TDRK算法比传统的RK算法更适用于大步长、长时间的高效数值模拟。

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