热带平衡和模式简化的一种约束求解方法
A Constraint Solving Approach to Tropical Equilibration and Model Reduction
摘要：
模型降阶是系统生物学和动力系统理论中的一个中心课题，用于降低详细模型的复杂性，寻找重要参数，以及开发多尺度模型。虽然微扰理论是分析动力系统的不同时间尺度并相应地分解系统的标准数学工具，但热带方法提供了一个简单的代数框架，可以在多项式系统中系统地执行这些分析。这些热带化方法的关键在于热带平衡的计算。在本文中，我们表明，基于约束的方法，使用具体化的约束表示的平衡条件，使它有可能数值求解非线性热带平衡问题，达到标准的计算方法。我们首先通过简化简单的生化机制（如Michaelis-Menten和Goldbeter-Koshland模型）来说明这种方法，其次，通过在模型库\texttt{biomodels.net}上大规模获得的性能数据来说明这种方法
英文摘要：
Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a standard mathematical tool to analyze the different time scales of a dynamical system, and decompose the system accordingly, tropical methods provide a simple algebraic framework to perform these analyses systematically in polynomial systems. The crux of these tropicalization methods is in the computation of tropical equilibrations. In this paper we show that constraint-based methods, using reified constraints for expressing the equilibration conditions, make it possible to numerically solve non-linear tropical equilibration problems, out of reach of standard computation methods. We illustrate this approach first with the reduction of simple biochemical mechanisms such as the Michaelis-Menten and Goldbeter-Koshland models, and second, with performance figures obtained on a large scale on the model repository \texttt{biomodels.net}
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