Gasparyan Manvel, Rao Shodhan
School of Environmental Engineering, University of Seoul, Seoul 02504, Republic of Korea.
Center for Biosystems and Biotech Data Science, Ghent University Global Campus, Incheon 21985, Republic of Korea.
Bioengineering (Basel). 2023 Sep 7;10(9):1056. doi: 10.3390/bioengineering10091056.
The current manuscript addresses the problem of parameter estimation for kinetic models of chemical reaction networks from observed time series partial experimental data of species concentrations. It is demonstrated how the Kron reduction method of kinetic models, in conjunction with the (weighted) least squares optimization technique, can be used as a tool to solve the above-mentioned ill-posed parameter estimation problem. First, a new trajectory-independent measure is introduced to quantify the dynamical difference between the original mathematical model and the corresponding Kron-reduced model. This measure is then crucially used to estimate the parameters contained in the kinetic model so that the corresponding values of the species' concentrations predicted by the model fit the available experimental data. The new parameter estimation method is tested on two real-life examples of chemical reaction networks: nicotinic acetylcholine receptors and Trypanosoma brucei trypanothione synthetase. Both weighted and unweighted least squares techniques, combined with Kron reduction, are used to find the best-fitting parameter values. The method of leave-one-out cross-validation is utilized to determine the preferred technique. For nicotinic receptors, the training errors due to the application of unweighted and weighted least squares are 3.22 and 3.61 respectively, while for Trypanosoma synthetase, the application of unweighted and weighted least squares result in training errors of 0.82 and 0.70 respectively. Furthermore, the problem of identifiability of dynamical systems, i.e., the possibility of uniquely determining the parameters from certain types of output, has also been addressed.
当前手稿探讨了从物种浓度的观测时间序列部分实验数据中估计化学反应网络动力学模型参数的问题。本文展示了动力学模型的Kron约简方法与（加权）最小二乘优化技术相结合，如何用作解决上述不适定参数估计问题的工具。首先，引入了一种新的与轨迹无关的度量，以量化原始数学模型与相应的Kron约简模型之间的动力学差异。然后，该度量被关键地用于估计动力学模型中包含的参数，以使模型预测的物种浓度的相应值拟合可用的实验数据。新的参数估计方法在化学反应网络的两个实际例子上进行了测试：烟碱型乙酰胆碱受体和布氏锥虫锥虫硫醇合成酶。加权和非加权最小二乘技术与Kron约简相结合，用于找到最佳拟合参数值。留一法交叉验证方法用于确定首选技术。对于烟碱型受体，应用非加权和加权最小二乘的训练误差分别为3.22和3.61，而对于锥虫硫醇合成酶，应用非加权和加权最小二乘的训练误差分别为0.82和0.70。此外，还讨论了动态系统的可识别性问题，即从某些类型的输出唯一确定参数的可能性。
