Graph-Based Proofs of Indistinguishability of Linear Compartmental Models

TL;DR

This paper introduces a graph-theoretic approach to proving indistinguishability of linear compartmental models, providing a new perspective that replaces previous linear algebra-based proofs.

Contribution

It reestablishes indistinguishability results for skeletal path models using graph theory, offering a novel proof technique.

Findings

Graph-theoretic proofs for model indistinguishability

Reproves previous algebraic results with a new framework

Enhances understanding of model equivalence in biological systems

Abstract

Given experimental data, one of the main objectives of biological modeling is to construct a model which best represents the real world phenomena. In some cases, there could be multiple distinct models exhibiting the exact same dynamics, meaning from the modeling perspective it would be impossible to distinguish which model is ``correct.'' This is the study of indistinguishability of models, and in our case we focus on linear compartmental models which are often used to model pharmacokinetics, cell biology, ecology, and related fields. Specifically, we focus on a family of linear compartmental models called skeletal path models which have an underlying directed path, and have recently been shown to have the first recorded sufficient conditions for indistinguishability based on underlying graph structure. In this recent work, certain families of skeletal path models were proven to be indistinguishable, however the proofs relied heavily on linear algebra. In this work, we reprove several of these indistinguishability results instead using a graph theoretic framework.