Identifiability Results for Several Classes of Linear Compartment Models.
Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, 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 this work, we study linear compartment models, which are a class of biological models commonly used in pharmacokinetics, physiology, and ecology. In past work, we used commutative algebra and graph theory to identify a class of linear compartment models that we call identifiable cycle models, which are unidentifiable 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.
Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC, 27695-8205, USA. nmeshkat@scu.edu.
Nicolette
N
Meshkat
Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC, 27695-8205, USA. smsulli2@ncsu.edu.
Seth
S
Sullivant
Departments of Epidemiology and Mathematics, University of Michigan, Ann Arbor, MI, 48109-2029, USA. marisae@umich.edu.
Marisa
M
Eisenberg
D000818:Animals; D011992:Endosomes / Q000378:metabolism; D006801:Humans; D016014:Linear Models; D008345:Manganese / Q000493:pharmacokinetics; D055641:Mathematical Concepts; D008954:Models, Biological; D051381:Rats
D008345:Manganese
Differential algebra; Identifiability; Identifiable functions; Linear compartment models