Which Small Reaction Networks Are Multistationary?
Which Small Reaction Networks Are Multistationary?
复制标题
哪些小反应网络是多平稳的？
DOI：
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复制
发表时间：
2016
影响因子：
2.1
通讯作者：
Anne Shiu
中科院分区：
文献类型：
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作者：
Badal Joshi;Anne Shiu
从流行病学到群体生物学，再到化学反应系统，反应网络与质量作用动力学一起出现在许多环境中。双稳态反应网络被假定为生化开关的基础，这激发了以下问题：哪些反应网络具有多个稳态的能力？数学上，这问：在某些参数化的家庭多项式系统，其中承认多个正根？没有完整的答案是已知的。这项工作分析了最小的网络，即只有少数化学物质或反应的网络。对于这些“最小”网络，我们完全回答了多平稳性的问题，在某些情况下，也是多稳定性，从而扩展了Boros的相关工作。我们的结果突出了网络的牛顿多面体（反应物向量的凸船体）所起的作用。此外，我们的工作的动机是最近的结果，解释了如何一个给定的网络的多平稳性的能力产生的某些相关的网络，通常是较小的。因此，我们有兴趣对小型多稳态网络进行分类，我们的工作是朝着这个方向迈出的第一步。
Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. Bistable reaction networks are posited to underlie biochemical switches, which motivates the following question: which reaction networks have the capacity for multiple steady states? Mathematically, this asks: among certain parametrized families of polynomial systems, which admit multiple positive roots? No complete answer is known. This work analyzes the smallest networks, those with only a few chemical species or reactions. For these "smallest" networks, we completely answer the question of multistationarity and, in some cases, multistability too, thereby extending related work of Boros. Our results highlight the role played by the Newton polytope of a network (the convex hull of the reactant vectors). Also, our work is motivated by recent results that explain how a given network's capacity for multistationarity arises from that of certain related networks which are typically smaller. Hence, we are interested in classifying small multistationary networks, and our work forms a first step in this direction.