@article{bortner_meshkat_2022, title={Identifiable Paths and Cycles in Linear Compartmental Models}, volume={84}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-022-01007-5}, abstractNote={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.}, number={5}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Bortner, Cashous and Meshkat, Nicolette}, year={2022}, month={May} }
@article{meshkat_sullivant_eisenberg_2015, title={Identifiability Results for Several Classes of Linear Compartment Models}, volume={77}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-015-0098-0}, abstractNote={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.}, number={8}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Meshkat, Nicolette and Sullivant, Seth and Eisenberg, Marisa}, year={2015}, month={Aug}, pages={1620–1651} }
@article{meshkat_sullivant_2014, title={Identifiable reparametrizations of linear compartment models}, volume={63}, ISSN={["0747-7171"]}, DOI={10.1016/j.jsc.2013.11.002}, abstractNote={Structural identifiability concerns finding which unknown parameters of a model can be quantified from given input–output data. Many linear ODE models, used in systems biology and pharmacokinetics, are unidentifiable, which means that parameters can take on an infinite number of values and yet yield the same input–output data. We use commutative algebra and graph theory to study a particular class of unidentifiable models and find conditions to obtain identifiable scaling reparametrizations of these models. Our main result is that the existence of an identifiable scaling reparametrization is equivalent to the existence of a scaling reparametrization by monomial functions. We provide an algorithm for finding these reparametrizations when they exist and partial results beginning to classify graphs which possess an identifiable scaling reparametrization.}, journal={JOURNAL OF SYMBOLIC COMPUTATION}, author={Meshkat, Nicolette and Sullivant, Seth}, year={2014}, month={May}, pages={46–67} }
@article{mahdi_meshkat_sullivant_2014, title={Structural Identifiability of Viscoelastic Mechanical Systems}, volume={9}, ISSN={["1932-6203"]}, DOI={10.1371/journal.pone.0086411}, abstractNote={We solve the local and global structural identifiability problems for viscoelastic mechanical models represented by networks of springs and dashpots. We propose a very simple characterization of both local and global structural identifiability based on identifiability tables, with the purpose of providing a guideline for constructing arbitrarily complex, identifiable spring-dashpot networks. We illustrate how to use our results in a number of examples and point to some applications in cardiovascular modeling.}, number={2}, journal={PLOS ONE}, author={Mahdi, Adam and Meshkat, Nicolette and Sullivant, Seth}, year={2014}, month={Feb} }