Identifiability results for several classes of linear compartment models

TL;DR

This paper investigates conditions under which linear compartment models are identifiable from input-output data, proposing modifications and combinations of models to achieve identifiability, with applications to biological systems.

Contribution

It introduces methods to modify and combine identifiable cycle models to ensure their identifiability, expanding the class of models that can be reliably estimated from data.

Findings

Adding inputs or outputs can make models identifiable.

Combining strongly connected models yields larger identifiable models.

Applied results to biological models from various fields.

Abstract

Identifiability concerns finding which unknown parameters of a model can be estimated from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is unidentifiable. In past work we identified a class of models, that we call identifiable cycle models, which are not identifiable but have the simplest possible identifiable functions (so-called monomial cycles). Here we show how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that we obtain an identifiable model. We also prove a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model. We apply these theoretical results to several real-world biological models from physiology, cell biology, and ecology.