Identifiable Paths and Cycles in Linear Compartmental Models

Abstract

We introduce a class of linear compartmental models called identifiable path/cycle models which have the property that all of the monomial functions of parameters associated to the directed cycles and paths from input compartments to output compartments are identifiable and give sufficient conditions to obtain an identifiable path/cycle model. Removing leaks, we then show how one can obtain a locally identifiable model from an identifiable path/cycle model. These identifiable path/cycle models yield the only identifiable models with certain conditions on their graph structure and thus we provide necessary and sufficient conditions for identifiable models with certain graph properties. A sufficient condition based on the graph structure of the model is also provided so that one can test if a model is an identifiable path/cycle model by examining the graph itself. We also provide some necessary conditions for identifiability based on graph structure. Our proofs use algebraic and combinatorial techniques.

A Kinetic Finite Volume Discretization of the Multidimensional PIDE Model for Gene Regulatory Networks

“…Anderson 2013 ; Berman and Plemmons 1994 ; Meshkat et al. 2015 ; Bortner and Meshkat 2022 ). Another important related family of models is the class of chemical reaction networks (CRNs) or kinetic systems which includes dynamical models that can be formally represented by a set of transformations (reactions) between abstract chemical complexes.…”