A constrained wavelet smoother for pathway identification tasks in systems biology

Metabolic time series data are being generated with increasing frequency, because they contain enormous information about the pathway from which the metabolites derive. This information is not directly evident, though, and must be extracted with advanced computational means. One typical step of this extraction is the estimation of slopes of the time courses from the data. Since the data are almost always noisy, and the noise is typically amplified in the slopes, this step can become a critical bottleneck. Several smoothers have been proposed in the literature for this purpose, but they all face the potential problem that smoothed time series data no longer correspond to a system that conserves mass throughout the measurement time period. To counteract this issue, we are proposing here a smoother that is based on wavelets and, through an iterative process, converges to a mass-conserving, smooth representation of the metabolic data. The degree of smoothness is user defined. We demonstrate the method with some didactic examples and with the analysis of actual measurements characterizing the glycolytic pathway in the dairy bacterium Lactococcus lactis. MATLAB code for the constrained smoother is available as a Supplement.