Automated smoother for the numerical decoupling of dynamics models

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.The reverse engineering of biological systems from experimental data often cannot be achieved on first principles. This is as much a reflection of the lack of plausible hypotheses as it is an indication of excessive parametric sensitivity when alleged mechanistic formulations are at hand. Consequently, there is a critical need for a description of dynamic behaviors that can be used as a machine learning tool (e.g., as a generic "black box"), but with parameters capable of shedding light on the topology of the underlying mechanisms. Biochemical Systems Theory [1-3], offers such formalism, especially in the form of S-systems, where kinetic-order coefficients characterize the topology of a biological network as well as the magnitude of each interaction. A drawback of this approach is that the parameterization of S-systems is a difficult problem, even for five metabolic species [4]. In a previous report