title: Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.
abstract: The steady states of cells affect their response to perturbation. Indeed, diagnostic markers for predicting the response to therapeutic perturbation are often based on steady state measurements. In spite of this, no method exists to systematically characterize the relationship between steady state and response. Mathematical models are established tools for studying cellular responses, but characterizing their relationship to the steady state requires that it have a parametric, or analytical, expression. For some models, this expression can be derived by the King-Altman method. However, King-Altman requires that no substrate act as an enzyme, and is therefore not applicable to most models of signal transduction. For this reason we developed py-substitution, a simple but general method for deriving analytical expressions for the steady states of mass action models. Where the King-Altman method is applicable, we show that py-substitution yields an equivalent expression, and at comparable efficiency. We use py-substitution to study the relationship between steady state and sensitivity to the anti-cancer drug candidate, dulanermin (recombinant human TRAIL). First, we use py-substitution to derive an analytical expression for the steady state of a published model of TRAIL-induced apoptosis. Next, we show that the amount of TRAIL required for cell death is sensitive to the steady state concentrations of procaspase 8 and its negative regulator, Bar, but not the other procaspase molecules. This suggests that activation of caspase 8 is a critical point in the death decision process. Finally, we show that changes in the threshold at which TRAIL results in cell death is not always equivalent to changes in the time of death, as is commonly assumed. Our work demonstrates that an analytical expression is a powerful tool for identifying steady state determinants of the cellular response to perturbation. All code is available at http://signalingsystems.ucsd.edu/models-and-code/ or as supplementary material accompanying this paper.
authors.affiliation: Signaling Systems Laboratory, Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California, United States of America.
authors.forename: Paul Michael
authors.initials: PM
authors.lastname: Loriaux
authors.forename: Glenn
authors.initials: G
authors.lastname: Tesler
authors.forename: Alexander
authors.initials: A
authors.lastname: Hoffmann
mesh_terms: D000970:Antineoplastic Agents / Q000494:pharmacology; D053181:Caspase 8 / Q000737:chemistry / Q000378:metabolism; D016923:Cell Death / Q000187:drug effects / Q000502:physiology; D019295:Computational Biology / Q000379:methods*; D006367:HeLa Cells; D006801:Humans; D007700:Kinetics; D008954:Models, Biological; D015398:Signal Transduction / Q000502:physiology*; D053221:TNF-Related Apoptosis-Inducing Ligand / Q000494:pharmacology
chemical_list: D000970:Antineoplastic Agents; D053221:TNF-Related Apoptosis-Inducing Ligand; C505653:TNFSF10 protein, human; D053181:Caspase 8