Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.

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 a...

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Autores principales: Paul Michael Loriaux, Glenn Tesler, Alexander Hoffmann
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Publicado: Public Library of Science (PLoS) 2013
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spelling oai:doaj.org-article:8b4f81f5592a46fa801ca490a4ebc89c2021-11-18T05:52:24ZCharacterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.1553-734X1553-735810.1371/journal.pcbi.1002901https://doaj.org/article/8b4f81f5592a46fa801ca490a4ebc89c2013-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/23509437/pdf/?tool=EBIhttps://doaj.org/toc/1553-734Xhttps://doaj.org/toc/1553-7358The 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.Paul Michael LoriauxGlenn TeslerAlexander HoffmannPublic Library of Science (PLoS)articleBiology (General)QH301-705.5ENPLoS Computational Biology, Vol 9, Iss 2, p e1002901 (2013)
institution DOAJ
collection DOAJ
language EN
topic Biology (General)
QH301-705.5
spellingShingle Biology (General)
QH301-705.5
Paul Michael Loriaux
Glenn Tesler
Alexander Hoffmann
Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.
description 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.
format article
author Paul Michael Loriaux
Glenn Tesler
Alexander Hoffmann
author_facet Paul Michael Loriaux
Glenn Tesler
Alexander Hoffmann
author_sort Paul Michael Loriaux
title Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.
title_short Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.
title_full Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.
title_fullStr Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.
title_full_unstemmed Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.
title_sort characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.
publisher Public Library of Science (PLoS)
publishDate 2013
url https://doaj.org/article/8b4f81f5592a46fa801ca490a4ebc89c
work_keys_str_mv AT paulmichaelloriaux characterizingtherelationshipbetweensteadystateandresponseusinganalyticalexpressionsforthesteadystatesofmassactionmodels
AT glenntesler characterizingtherelationshipbetweensteadystateandresponseusinganalyticalexpressionsforthesteadystatesofmassactionmodels
AT alexanderhoffmann characterizingtherelationshipbetweensteadystateandresponseusinganalyticalexpressionsforthesteadystatesofmassactionmodels
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