Cell signaling pathways, which are a series of reactions that start at receptors and end at transcription factors, are basic to systems biology. Properly modeling the reactions in such pathways requires directed hypergraphs, where an edge is now directed between two sets of vertices. Inferring a pathway by the most parsimonious series of reactions corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete. The current state-of-the-art for shortest hyperpaths in cell signaling hypergraphs solves a mixed-integer linear program to find an optimal hyperpath that is restricted to be acyclic, and offers no efficiency guarantees. We present, for the first time, a heuristic for general shortest hyperpaths that properly handles cycles, and is guaranteed to be efficient. We show the heuristic finds provably optimal hyperpaths for the class of singleton-tail hypergraphs, and also give a practical algorithm for tractably generating all source-sink hyperpaths. The accuracy of the heuristic is demonstrated through comprehensive experiments on all source-sink instances from the standard NCI-PID and Reactome pathway databases, which show it finds a hyperpath that matches the state-of-the-art mixed-integer linear program on over 99% of all instances that are acyclic. On instances where only cyclic hyperpaths exist, the heuristic surpasses the state-of-the-art, which finds no solution; on every such cyclic instance, enumerating all source-sink hyperpaths shows the solution found by the heuristic was in fact optimal. The new shortest hyperpath heuristic is both fast and accurate. This makes finding source-sink hyperpaths, which in general may contain cycles, now practical for real cell signaling networks. Source code for the hyperpath heuristic in a new tool we call Hhugin (as well as for hyperpath enumeration, and all dataset instances) is available free for non-commercial use at http://hhugin.cs.arizona.edu.

中文翻译：

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细胞信号超图中的启发式最短超路径

细胞信号通路是一系列从受体开始到转录因子结束的反应，是系统生物学的基础。正确模拟此类路径中的反应需要有向超图，其中一条边现在指向两组顶点之间。通过最简约的一系列反应推断路径对应于在有向超图中找到最短的超路径，这是 NP 完全的。细胞信号超图中最短超路径的当前最新技术解决了混合整数线性程序，以找到限制为非循环的最佳超路径，并且不提供效率保证。我们首次提出了一种通用最短超路径的启发式方法，可以正确处理循环，并保证高效。我们展示了启发式发现可证明的单尾超图类的最佳超路径，并提供了一种实用的算法来轻松生成所有源汇超路径。通过对来自标准 NCI-PID 和 Reactome 路径数据库的所有源-汇实例的综合实验证明了启发式算法的准确性，这表明它找到了一个与最先进的混合整数线性程序相匹配的超路径。 99% 的实例是非循环的。在仅存在循环超路径的情况下，启发式算法超越了最先进的技术，后者找不到解决方案；在每个这样的循环实例上，枚举所有源汇超路径表明启发式找到的解决方案实际上是最优的。新的最短超路径启发式算法既快速又准确。这使得寻找源汇超路径，通常可能包含循环，现在可用于真实的小区信令网络。我们称为 Hhugin 的新工具中超路径启发式的源代码（以及超路径枚举和所有数据集实例）可在 http://hhugin.cs.arizona.edu 免费用于非商业用途。