On the Parameter Combinations That Matter and on Those That do Not

We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the dynamic output behavior: a set of effective parameters for the model. Furthermore, we use Conformal Autoencoder Neural Networks, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters, nonlinear combinations of the physical ones, has previously been established analytically.