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Computational and Mathematical Methods in Medicine
Volume 2017, Article ID 3020326, 9 pages
https://doi.org/10.1155/2017/3020326
Research Article

Inference of Biochemical S-Systems via Mixed-Variable Multiobjective Evolutionary Optimization

1School of Science, Wuhan University of Technology, Wuhan, Hubei 430070, China
2School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China

Correspondence should be addressed to Yu Chen; nc.ude.tuhw@nehcy

Received 30 November 2016; Accepted 27 April 2017; Published 21 May 2017

Academic Editor: Giancarlo Ferrigno

Copyright © 2017 Yu Chen 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

Inference of the biochemical systems (BSs) via experimental data is important for understanding how biochemical components in vivo interact with each other. However, it is not a trivial task because BSs usually function with complex and nonlinear dynamics. As a popular ordinary equation (ODE) model, the S-System describes the dynamical properties of BSs by incorporating the power rule of biochemical reactions but behaves as a challenge because it has a lot of parameters to be confirmed. This work is dedicated to proposing a general method for inference of S-Systems by experimental data, using a biobjective optimization (BOO) model and a specially mixed-variable multiobjective evolutionary algorithm (mv-MOEA). Regarding that BSs are sparse in common sense, we introduce binary variables indicating network connections to eliminate the difficulty of threshold presetting and take data fitting error and the -norm as two objectives to be minimized in the BOO model. Then, a selection procedure that automatically runs tradeoff between two objectives is employed to choose final inference results from the obtained nondominated solutions of the mv-MOEA. Inference results of the investigated networks demonstrate that our method can identify their dynamical properties well, although the automatic selection procedure sometimes ignores some weak connections in BSs.