Open Access Open Badges Research article

Automated smoother for the numerical decoupling of dynamics models

Marco Vilela125*, Carlos CH Borges1, Susana Vinga3, Ana Tereza R Vasconcelos1, Helena Santos2, Eberhard O Voit4 and Jonas S Almeida25

Author Affiliations

1 Dept. Computatinal and Applied Mathematics, Laboratório Nacional de Computação Científica, Petrópolis, Rio de Janeiro, Brazil

2 Instituto de Tecnologia Química e Biológica, Universidade Nova de Lisboa, Rua da Quinta Grande 6, Apartado 127, 2780-156 Oeiras, Portugal

3 Instituto de Engenharia de Sistemas e Computadores: Investigação e Desenvolvimento (INESC-ID), R. Alves Redol 9, 1000-029 Lisboa, Portugal

4 Dept. Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

5 Dept. Bioinformatics and Computational Biology, M. D. Anderson Cancer Center, 1515 Holcombe Blvd, Houston, TX 77030, USA

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BMC Bioinformatics 2007, 8:305  doi:10.1186/1471-2105-8-305

Published: 21 August 2007



Structure identification of dynamic models for complex biological systems is the cornerstone of their reverse engineering. Biochemical Systems Theory (BST) offers a particularly convenient solution because its parameters are kinetic-order coefficients which directly identify the topology of the underlying network of processes. We have previously proposed a numerical decoupling procedure that allows the identification of multivariate dynamic models of complex biological processes. While described here within the context of BST, this procedure has a general applicability to signal extraction. Our original implementation relied on artificial neural networks (ANN), which caused slight, undesirable bias during the smoothing of the time courses. As an alternative, we propose here an adaptation of the Whittaker's smoother and demonstrate its role within a robust, fully automated structure identification procedure.


In this report we propose a robust, fully automated solution for signal extraction from time series, which is the prerequisite for the efficient reverse engineering of biological systems models. The Whittaker's smoother is reformulated within the context of information theory and extended by the development of adaptive signal segmentation to account for heterogeneous noise structures. The resulting procedure can be used on arbitrary time series with a nonstationary noise process; it is illustrated here with metabolic profiles obtained from in-vivo NMR experiments. The smoothed solution that is free of parametric bias permits differentiation, which is crucial for the numerical decoupling of systems of differential equations.


The method is applicable in signal extraction from time series with nonstationary noise structure and can be applied in the numerical decoupling of system of differential equations into algebraic equations, and thus constitutes a rather general tool for the reverse engineering of mechanistic model descriptions from multivariate experimental time series.