Use of a Generalized Fisher Equation for Global Optimization in Chemical Kinetics

Abstract

A new approach for parameter estimation in chemical kinetics has been recently proposed (Ross et al. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 12777). It makes use of an optimization criterion based on a Generalized Fisher Equation (GFE). Its utility has been demonstrated with two reaction mechanisms, the chlorite-iodide and Oregonator, which are computationally stiff systems. In this Article, the performance of the GFE-based algorithm is compared to that obtained from minimization of the squared distances between the observed and predicted concentrations obtained by solving the corresponding initial value problem (we call this latter approach "traditional" for simplicity). Comparison of the proposed GFE-based optimization method with the "traditional" one has revealed their differences in performance. This difference can be seen as a trade-off between speed (which favors GFE) and accuracy (which favors the traditional method). The chlorite-iodide and Oregonator systems are again chosen as case studies. An identifiability analysis is performed for both of them, followed by an optimal experimental design based on the Fisher Information Matrix (FIM). This allows to identify and overcome most of the previously encountered identifiability issues, improving the estimation accuracy. With the new data, obtained from optimally designed experiments, it is now possible to estimate effectively more parameters than with the previous data. This result, which holds for both GFE-based and traditional methods, stresses the importance of an appropriate experimental design. Finally, a new hybrid method that combines advantages from the GFE and traditional approaches is presented.