Some Investigations Concerning the CTMC and the ODE Model Derived From Bio-PEPA
Some Investigations Concerning the CTMC and the ODE Model Derived From Bio-PEPA
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DOI：
10.1016/j.entcs.2009.02.010
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发表时间：
2009-02-28
影响因子：
--
通讯作者：
Calder, Muffy
中科院分区：
文献类型：
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作者：
Ciocchetta, Federica;Degasperi, Andrea;Calder, Muffy
Bio-Pepa是最近定义的一种用于生化网络建模和分析的语言。它支持一种抽象的建模风格，在这种风格中，考虑的是物种内的离散浓度水平，而不是单个分子。系统的细粒度对应于较小的浓度步长，因此对应较多的浓度水平。这种类型的模型适用于各种不同的分析技术，包括基于CMTC的数值分析，其状态反映了浓度水平。此外，我们还研究了这种CTMC与由同一模型导出的常微分方程组之间的关系。利用Kurtz定理，我们证明了由Bio-Pepa模型导出的常微分方程组能够捕捉到从同一系统获得的CTMC的极限行为。最后，我们定义了一种经验方法来寻找Bio-Pepa系统的粒度，对于该系统，ODE和CTMC的水平是一致的。拟议的定义是基于两个模型之间的距离的概念。我们在一个具有振荡行为的简单生化网络Repressilator的模型上演示了我们的方法。
Bio-PEPA is a recently defined language for the modelling and analysis of biochemical networks. It supports an abstract style of modelling, in which discrete levels of concentration within a species are considered instead of individual molecules. A finer granularity for the system corresponds to a smaller concentration step size and therefore to a greater number of concentration levels. This style of model is amenable to a variety of different analysis techniques, including numerical analysis based on a CMTC with states reflecting the levels of concentration.In this paper we present a formal definition of the CTMC with levels derived from a Bio-PEPA system. Furthermore we investigate the relationship between this CTMC and the system of ordinary differential equations (ODEs) derived from the same model. Using Kurtz's theorem, we show that the set of ODEs derived from the Bio-PEPA model is able to capture the limiting behaviour of the CTMC obtained from the same system. Finally, we define an empirical methodology to find the granularity of the Bio-PEPA system for which the ODE and the CTMC with levels are in a good agreement. The proposed definition is based on a notion of distance between the two models. We demonstrate our approach on a model of the Repressilator, a simple biochemical network with oscillating behaviour.