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 tomore »
- Authors:
-
- University of California San Diego, La Jolla, CA (United States); San Diego Center for Systems Biology, La Jolla, CA (United States)
- University of California San Diego, La Jolla, CA (United States)
- Publication Date:
- Research Org.:
- University of California San Diego, La Jolla, CA (United States)
- Sponsoring Org.:
- USDOE; National Institutes of Health (NIH); National Science Foundation (NSF); San Diego Center for Systems Biology
- OSTI Identifier:
- 1904018
- Grant/Contract Number:
- GM072024; P50 GM085763; DMS-0718810; CCF-1115206
- Resource Type:
- Accepted Manuscript
- Journal Name:
- PLoS Computational Biology (Online)
- Additional Journal Information:
- Journal Name: PLoS Computational Biology (Online); Journal Volume: 9; Journal Issue: 2; Journal ID: ISSN 1553-7358
- Publisher:
- Public Library of Science
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; velocity; stoichiometry; vector spaces; adjustment of dosage at steady state; apoptosis; mitochondria; cell deaths; enzymes
Citation Formats
Loriaux, Paul Michael, Tesler, Glenn, and Hoffmann, Alexander. Characterizing the Relationship between Steady State and Response Using Analytical Expressions for the Steady States of Mass Action Models. United States: N. p., 2013.
Web. doi:10.1371/journal.pcbi.1002901.
Loriaux, Paul Michael, Tesler, Glenn, & Hoffmann, Alexander. Characterizing the Relationship between Steady State and Response Using Analytical Expressions for the Steady States of Mass Action Models. United States. https://doi.org/10.1371/journal.pcbi.1002901
Loriaux, Paul Michael, Tesler, Glenn, and Hoffmann, Alexander. Thu .
"Characterizing the Relationship between Steady State and Response Using Analytical Expressions for the Steady States of Mass Action Models". United States. https://doi.org/10.1371/journal.pcbi.1002901. https://www.osti.gov/servlets/purl/1904018.
@article{osti_1904018,
title = {Characterizing the Relationship between Steady State and Response Using Analytical Expressions for the Steady States of Mass Action Models},
author = {Loriaux, Paul Michael and Tesler, Glenn and Hoffmann, Alexander},
abstractNote = {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.},
doi = {10.1371/journal.pcbi.1002901},
journal = {PLoS Computational Biology (Online)},
number = 2,
volume = 9,
place = {United States},
year = {Thu Feb 28 00:00:00 EST 2013},
month = {Thu Feb 28 00:00:00 EST 2013}
}
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