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Computational and Mathematical Methods in Medicine
Volume 2013, Article ID 698341, 8 pages
http://dx.doi.org/10.1155/2013/698341
Research Article

Complexity Analysis and Parameter Estimation of Dynamic Metabolic Systems

1School of Information, Beijing Wuzi University, Beijing 101149, China
2School of Atuomation, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China
3Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK, Canada S7N 5A9
4Division of Biomedical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK, Canada S7N 5A9

Received 24 April 2013; Revised 18 August 2013; Accepted 5 September 2013

Academic Editor: Shengyong Chen

Copyright © 2013 Li-Ping Tian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A metabolic system consists of a number of reactions transforming molecules of one kind into another to provide the energy that living cells need. Based on the biochemical reaction principles, dynamic metabolic systems can be modeled by a group of coupled differential equations which consists of parameters, states (concentration of molecules involved), and reaction rates. Reaction rates are typically either polynomials or rational functions in states and constant parameters. As a result, dynamic metabolic systems are a group of differential equations nonlinear and coupled in both parameters and states. Therefore, it is challenging to estimate parameters in complex dynamic metabolic systems. In this paper, we propose a method to analyze the complexity of dynamic metabolic systems for parameter estimation. As a result, the estimation of parameters in dynamic metabolic systems is reduced to the estimation of parameters in a group of decoupled rational functions plus polynomials (which we call improper rational functions) or in polynomials. Furthermore, by taking its special structure of improper rational functions, we develop an efficient algorithm to estimate parameters in improper rational functions. The proposed method is applied to the estimation of parameters in a dynamic metabolic system. The simulation results show the superior performance of the proposed method.