  Design of experiments and model selection, though essential steps in data
science, are usually viewed as unrelated processes in the study and analysis of
biological networks. Not accounting for their inter-relatedness has the
potential to introduce bias and increase the risk of missing salient features
in the modeling process. We propose a data-driven computational framework to
unify experimental design and model selection for discrete data sets and
minimal polynomial models. We use a special affine transformation, called a
linear shift, to provide both the data sets and the polynomial terms that form
a basis for a model. This framework enables us to address two important
questions that arise in biological data science research: finding the data
which identify a set of known interactions and finding identifiable
interactions given a set of data. We present the theoretical foundation for a
web-accessible database. As an example, we apply this methodology to a
previously constructed pharmacodynamic model of epidermal derived growth factor
receptor (EGFR) signaling.
