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

Loriaux PM, Tesler G, Hoffmann A - PLoS Comput. Biol. (2013)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Signaling Systems Laboratory, Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California, United States of America.

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.

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The model of malate synthesis used to compare py-substitution with the King-Altman method.This mechanism for the conversion of fumarate to malate by the enzyme fumarase was proposed in [42]. Fumarase binds to fumarate and hydrogen in either order, then hydroxyl, followed by formation of the product, malate. All reactions are reversible. See “fum1.m” in Protocol S1 for a complete description of the model.
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pcbi-1002901-g003: The model of malate synthesis used to compare py-substitution with the King-Altman method.This mechanism for the conversion of fumarate to malate by the enzyme fumarase was proposed in [42]. Fumarase binds to fumarate and hydrogen in either order, then hydroxyl, followed by formation of the product, malate. All reactions are reversible. See “fum1.m” in Protocol S1 for a complete description of the model.

Mentions: Some chemical reaction systems are linear in the species concentration vector, or can be rendered linear by assuming that the concentrations of certain species don't change over time. The classical model for malate synthesis is an example of the latter [42]. Here, the enzyme fumarase binds reversibly to fumarate and hydrogen in either order, followed by reversible binding of hydroxyl and reversible formation of malate (Figure 3). The reactions for this model are


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

Loriaux PM, Tesler G, Hoffmann A - PLoS Comput. Biol. (2013)

The model of malate synthesis used to compare py-substitution with the King-Altman method.This mechanism for the conversion of fumarate to malate by the enzyme fumarase was proposed in [42]. Fumarase binds to fumarate and hydrogen in either order, then hydroxyl, followed by formation of the product, malate. All reactions are reversible. See “fum1.m” in Protocol S1 for a complete description of the model.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3585464&req=5

pcbi-1002901-g003: The model of malate synthesis used to compare py-substitution with the King-Altman method.This mechanism for the conversion of fumarate to malate by the enzyme fumarase was proposed in [42]. Fumarase binds to fumarate and hydrogen in either order, then hydroxyl, followed by formation of the product, malate. All reactions are reversible. See “fum1.m” in Protocol S1 for a complete description of the model.
Mentions: Some chemical reaction systems are linear in the species concentration vector, or can be rendered linear by assuming that the concentrations of certain species don't change over time. The classical model for malate synthesis is an example of the latter [42]. Here, the enzyme fumarase binds reversibly to fumarate and hydrogen in either order, followed by reversible binding of hydroxyl and reversible formation of malate (Figure 3). The reactions for this model are

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Signaling Systems Laboratory, Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California, United States of America.

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.

Show MeSH