An algorithm for identifiable parameters and parameter bounds for a class of cascaded mammillary models

Cellular signaling identifiability analysis: a case study

Two primary purposes for mathematical modeling in cell biology are (1) simulation for making predictions of experimental outcomes and (2) parameter estimation for drawing inferences from experimental data about unobserved aspects of biological systems. While the former purpose has become common in the biological sciences, the latter is less common, particularly when studying cellular and subcellular phenomena such as signaling-the focus of the current study. Data are difficult to obtain at this level. Therefore, even models of only modest complexity can contain parameters for which the available data are insufficient for estimation. In the present study, we use a set of published cellular signaling models to address issues related to global parameter identifiability. That is, we address the following question: assuming known time courses for some model variables, which parameters is it theoretically impossible to estimate, even with continuous, noise-free data? Following an introduction to this problem and its relevance, we perform a full identifiability analysis on a set of cellular signaling models using DAISY (Differential Algebra for the Identifiability of SYstems). We use our analysis to bring to light important issues related to parameter identifiability in ordinary differential equation (ODE) models. We contend that this is, as of yet, an under-appreciated issue in biological modeling and, more particularly, cell biology.

Thyroid hormone production rates in rat liver and intestine in vivo: a novel graph theory and experimental solution

We develop a novel method for finding sufficient experimental conditions for discriminating and quantifying individual biomolecule production sources in distributed, inhomogeneous multisource systems in vivo, and we apply it experimentally to a complex, unsolved problem in endocrinology. The majority of hormonal triiodothyronine (T3) is produced from prohormone thyroxine (T4) in numerous nonthyroidal organs and, with one exception, the T3 production rate has not been fully resolved in any single extrathyroidal organ of any species. Using a readily generalized graphic method called cut-set analysis, we show here that measured steady-state responses in several organs to three independent tracer infusions, two into blood and one directly into the organ(s) of interest, are sufficient to resolve this problem for organs fully accessible to direct infusion in vivo. We evaluated local T3 production in rat liver and intestine, which also required T3 bile flux measurements, and we found that liver produces approximately 31% and whole intestine approximately 6% of whole body T3 from T4. With thyroidal production included, liver contributes approximately 15% and intestine approximately 3% of whole rat T3 production. This new methodology is broadly applicable, especially to biosystems that include molecular interconversions at multiple sites.