化学计量定义的子网络中的多重正稳态 发电机

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摘要翻译：
在系统生物学中，一个给定的数学模型能否允许多个稳态的问题越来越引起人们的兴趣。由于参数值往往是未知的或具有很高的不确定性，人们常常关心一个问题，即给定的数学模型对于某个可想象的参数向量是否能表现出多平稳性。在Feinberg的亏一算法中给出了这个问题的部分答案。该算法可以通过分析与参数值无关的线性不等式系统来判断多平稳性。然而，亏一算法仅限于其作者所说的正则亏一网络。许多现实网络都存在一个以上的不足，因此该算法不能直接应用。在以前的一个出版物中，有人建议分析某些定义良好的子网络，这些子网络被保证是缺陷子网络。然而，现实的反应网络往往导致的子网络是不规则的，特别是如果考虑代谢网络。本文利用子网络的特殊结构导出了多平稳性的条件。这些条件与亏一算法所要求的正则性条件无关。因此，这些条件特别适用于不规则子网络。
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英文标题：
《Multiple positive steady states in subnetworks defined by stoichiometric
  generators》
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作者：
Carsten Conradi
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最新提交年份：
2009
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  In Systems Biology there is a growing interest in the question, whether or not a given mathematical model can admit more than one steady state. As parameter values are often unknown or subject to a very high uncertainty, one is often interested in the question, whether or not a given mathematical model can, for some conceivable parameter vector, exhibit multistationarity at all. A partial answer to this question is given in Feinberg's deficiency one algorithm. This algorithm can decide about multistationarity by analyzing systems of linear inequalities that are independent of parameter values. However, the deficiency one algorithm is limited to what its author calls regular deficiency one networks. Many realistic networks have a deficiency higher than one, thus the algorithm cannot be applied directly. In a previous publication it was suggested to analyze certain well defined subnetworks that are guaranteed to be of deficiency one. Realistic reaction networks, however, often lead to subnetworks that are irregular, especially if metabolic networks are considered. Here the special structure of the subnetworks is used to derive conditions for multistationarity. These conditions are independent of the regularity conditions required by the deficiency one algorithm. Thus, in particular, these conditions are applicable to irregular subnetworks.
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PDF链接：
https://arxiv.org/pdf/0909.4015

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关键词：发电机 Quantitative stationarity Mathematical inequalities 人们 steady 分析 subnetworks 无关