The genomic and post-genomic eras have been blessing us with overwhelming amounts of data that are of increasing quality. The challenge is that most of these data alone are mere snapshots of the functioning organism and do not reveal the organizational structure of which the particular genes and metabolites are contributors. To gain an appreciation of their roles and functions within cells and organisms, genomic and metabolic data need to be integrated in systems models that allow the testing of hypotheses, generate experimentally testable predictions, and ultimately lead to true explanations. One type of data that is particularly well suited for such integration consists of time profiles, which show gene activities, metabolite concentrations, or protein prevalences at dense series of time points. We show with a specific example how such time series can be analyzed and evaluated, if some structural information about the data is available, even if this information is incomplete. The method consists of three components. The first is a particularly suitable mathematical modeling framework, namely Biochemical Systems Theory, in which parameters are direct indicators of the organization of the underlying phenomenon, the second is the training of an artificial neural network for data smoothing and complementation, and the third is a technique for reinterpreting differential equations in a fashion that facilitates parameter estimation. A prototype webtool for these analyses is available at https://bioinformatics.musc.edu/webmetabol/.