Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.
Characterizing the relationship between steady state and response using analytical expressions for the steady states of mass action models.
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DOI：
10.1371/journal.pcbi.1002901
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发表时间：
2013
影响因子：
4.3
通讯作者：
Hoffmann A
中科院分区：
文献类型：
--
作者：
Loriaux PM;Tesler G;Hoffmann A
细胞的稳定状态影响它们对扰动的反应。事实上，用于预测对治疗性扰动反应的诊断标记通常基于稳态测量。尽管如此，还没有办法系统地描述稳态和响应之间的关系。数学模型是研究细胞反应的工具，但描述它们与稳态的关系需要有一个参数化的或解析的表达。对于某些模型，可以用King-Altman方法推导出这个表达式。然而，King-Altman要求没有底物作为酶，因此不适用于大多数信号转导模型。为此，我们开发了一种简单而通用的方法——p -代换法，用于推导质量作用模型稳态的解析表达式。在King-Altman方法适用的情况下，我们证明了py替换产生一个等价表达式，并且效率相当。我们使用y-取代来研究稳态与抗癌候选药物dulanermin（重组人TRAIL）敏感性之间的关系。首先，我们使用py取代法推导出已发表的trail诱导细胞凋亡模型稳态的解析表达式。接下来，我们发现细胞死亡所需的TRAIL量对procaspase 8及其负调节因子Bar的稳态浓度敏感，但对其他procaspase分子不敏感。这表明caspase 8的激活在死亡决定过程中是一个关键点。最后，我们表明，TRAIL导致细胞死亡的阈值的变化并不总是等同于死亡时间的变化，正如通常假设的那样。我们的工作表明，解析表达式是识别细胞对扰动反应的稳态决定因素的有力工具。所有代码可在http://signalingsystems.ucsd.edu/models-and-code/或作为本文的补充材料获得。诊断标记来源于稳态测量，但用于预测细胞对治疗的反应。为了开发新的和更好的诊断方法，我们希望系统地描述稳态和对给定治疗的反应之间的关系。在这方面，数学模型有力地补充了实证研究，但使用这些模型来表征稳态的影响仍然具有挑战性。要做到这一点，需要一个稳态的数学表达式，而目前还没有一个通用的方法。在这里，我们提出了一种方法来推导一类常见模型的稳态数学表达式，这些模型服从质量作用定律。结果表明，该方法易于使用，适用于大型模型。然后，我们用我们的方法来表征稳态和对抗癌候选药物dulanermin敏感性之间的关系。我们发现对药物的敏感性受到信号分子procaspase 8及其抑制剂Bar浓度的强烈影响。因此，我们的工作证明了稳态及其与药物敏感性关系的分析研究的实用性。
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. Diagnostic markers are derived from steady state measurements, but are used to predict the cellular response to therapy. To develop new and better diagnostics, we would like to systematically characterize the relationship between steady state and the response to a given therapeutic. Mathematical models have powerfully complemented empirical studies in this regard, but it remains challenging to employ these models to characterize the effects of steady state. To do so requires a mathematical expression for the steady state, for which no universal method has been developed. Here, we present a method for deriving a mathematical expression for the steady state of a common class of models, those that obey the Law of Mass Action. We show that our method is easy to use and scales well to large models. We then use our method to characterize the relationship between steady state and the sensitivity to the anti-cancer drug candidate, dulanermin. We find that sensitivity to the drug is strongly affected by the concentration of the signaling molecule, procaspase 8, and its inhibitor, Bar. Our work thus demonstrates the utility of analytical studies of the steady state and its relationship to drug sensitivity.
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影响因子：
3.5
作者：
Feliu, Elisenda;Knudsen, Michael;Wiuf, Carsten
通讯作者：
Wiuf, Carsten
影响因子：
9.8
作者：
Albeck JG;Burke JM;Spencer SL;Lauffenburger DA;Sorger PK
通讯作者：
Sorger PK
影响因子：
9.9
作者：
Cheong, Raymond;Hoffmann, Alexander;Levchenko, Andre
通讯作者：
Levchenko, Andre
DOI：
10.1002/wsbm.60
发表时间：
2010-05-01
影响因子：
7.9
作者：
Gianchandani, Erwin P.;Chavali, Arvind K.;Papin, Jason A.
通讯作者：
Papin, Jason A.
影响因子：
12.4
作者：
Ganten, TM;Haas, TL;Walczak, H
通讯作者：
Walczak, H