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

TL;DR

This paper introduces a data-driven method using Diffusion Maps and neural networks to identify minimal effective parameters in kinetic models, distinguishing influential parameter combinations from redundant ones for better system understanding.

Contribution

It presents a novel combination of Diffusion Maps, Conformal Autoencoders, and kernel techniques to characterize parameter nonidentifiability and extract effective parameters in kinetic models.

Findings

Successfully identified minimal effective parameters in kinetic models.

Validated approach on multisite phosphorylation model.

Enhanced interpretability and utility for behavior prediction and parameter estimation.

Abstract

We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, 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.