Wu Fang-Xiang, Mu Lei
Department of Mechanical Engineering and associated with Division of Biomedical Engineering in the University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada.
Annu Int Conf IEEE Eng Med Biol Soc. 2009;2009:3263-6. doi: 10.1109/IEMBS.2009.5333508.
Based on statistical thermodynamics or Michaelis -Menten kinetics, molecular biological systems can be modeled by a system of nonlinear differential equations. The nonlinearity in the model stems from rational reaction rates whose numerator and denominator are linear in parameters. It is a nonlinear problem to estimate the parameters in such rational models of molecular biological systems. In principle, any nonlinear optimization methods such as Newton-Gauss method and its variants can be used to estimate parameters in the rational models. However, these methods may converge to a local minimum and be sensitive to the initial values. In this study, we propose a new method to estimate the parameters in the rational models of molecular biological systems. In the proposed method, the cost function in all parameters is first reduced to a cost function only in the parameters in the denominator by a separable theorem. Then the parameters in the denominator are estimated by minimizing this cost function using our proposed new iteration method. Finally, the parameters in the numerator are estimated by a well defined linear least squares formula. A simple gene regulatory system is used as an example to illustrate the performance of the proposed method. Simulation results show that the proposed method performs better than the general nonlinear optimization methods in terms of the running time, robustness (insensitivity) to the initial values, and the accuracy of estimates.
基于统计热力学或米氏动力学，分子生物学系统可以用一个非线性微分方程组来建模。模型中的非线性源于合理的反应速率，其分子和分母在参数上是线性的。在这种分子生物学系统的合理模型中估计参数是一个非线性问题。原则上，任何非线性优化方法，如牛顿 - 高斯方法及其变体，都可用于估计合理模型中的参数。然而，这些方法可能会收敛到局部最小值，并且对初始值敏感。在本研究中，我们提出了一种新方法来估计分子生物学系统合理模型中的参数。在所提出的方法中，首先通过一个可分离定理将所有参数的代价函数简化为仅关于分母中参数的代价函数。然后使用我们提出的新迭代方法通过最小化这个代价函数来估计分母中的参数。最后，通过一个定义明确的线性最小二乘公式来估计分子中的参数。以一个简单的基因调控系统为例来说明所提方法的性能。仿真结果表明，所提方法在运行时间、对初始值的鲁棒性（不敏感性）和估计精度方面比一般的非线性优化方法表现更好。
