化学反应网络的超图定向拟阵关系依赖流模型
Hypergraphic Oriented Matroid Relational Dependency Flow Models of Chemical Reaction Networks
摘要：
在本文中，我们推导出并提出了一个应用程序的超图定向拟阵的目的是枚举变量的相互依赖关系，定义与非线性动力系统表示的化学动力学反应流网络的动力学化学复合物。通过在符号多重集的n-子集族上定义一个闭包算子，得到了一个超图定向拟阵的导子，并由此得到了一个Z-模.已经观察到，符号多重集族上的闭包算子的每个实例定义了拟阵结构。然后证明了这些结构产生一对对偶拟阵，分别对应于从相应的有向超图得到的超生成树和超圈。接下来系统地评估这些结构以获得满足MAP激酶级联细胞信号传导途径中的非线性化学动力学反应流网络系统的解集。
英文摘要：
In this paper we derive and present an application of hypergraphic oriented matroids for the purpose of enumerating the variable interdependencies that define the chemical complexes associated with the kinetics of non-linear dynamical system representations of chemical kinetic reaction flow networks. The derivation of a hypergraphic oriented matroid is obtained by defining a closure operator on families of n-subsets of signed multi-sets from which a "Z-module" is obtained. It has been observed that every instantiation of the closure operator on the signed multiset families define a matroid structure. It is then demonstrated that these structures generate a pair of dual matroids corresponding respectively to hyperspanning trees and hypercycles obtained from the corresponding directed hypergraphs. These structures are next systematically evaluated to obtain solution sets that satisfy systems of non-linear chemical kinetic reaction flow networks in the MAP Kinase cascade cell-signaling pathway.
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