Signaling and metabolic pathways, which consist of chains of reactions that produce target molecules from source compounds, are cornerstones of cellular biology. Properly modeling the reaction networks that represent such pathways requires directed hypergraphs, where each molecule or compound maps to a vertex, and each reaction maps to a hyperedge directed from its set of input reactants to its set of output products. Inferring the most likely series of reactions that produces a given set of targets from a given set of sources, where for each reaction its reactants are produced by prior reactions in the series, corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete. We give the first exact algorithm for general shortest hyperpaths that can find provably optimal solutions for large, real-world, reaction networks. In particular, we derive a novel graph-theoretic characterization of hyperpaths, which we leverage in a new integer linear programming formulation of shortest hyperpaths that for the first time handles cycles, and develop a cutting-plane algorithm that can solve this integer linear program to optimality in practice. Through comprehensive experiments over all of the thousands of instances from the standard Reactome and NCI-PID reaction databases, we demonstrate that our cutting-plane algorithm quickly finds an optimal hyperpath-inferring the most likely pathway-with a median running time of under 10 seconds, and a maximum time of less than 30 minutes, even on instances with thousands of reactions. We also explore for the first time how well hyperpaths infer true pathways, and show that shortest hyperpaths accurately recover known pathways, typically with very high precision and recall. Source code implementing our cutting-plane algorithm for shortest hyperpaths is available free for research use in a new tool called Mmunin.

中文翻译：

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用于反应路径推断的有向超图中的最短超路径。

信号传导和代谢途径由从源化合物产生目标分子的反应链组成，是细胞生物学的基石。正确建模代表此类路径的反应网络需要有向超图，其中每个分子或化合物映射到一个顶点，每个反应映射到从其输入反应物集到其输出产物集的超边。推断从给定的一组源产生一组给定的目标的最可能的反应系列，其中对于每个反应，其反应物是由该系列中的先前反应产生的，对应于在有向超图中找到最短的超路径，即 NP -完全的。我们给出了第一个针对一般最短超路径的精确算法，该算法可以为大型、现实世界的反应网络找到可证明的最佳解决方案。特别是，我们推导了一种新颖的超路径图论表征，我们在最短超路径的新整数线性规划公式中利用它，首次处理循环，并开发了一种割平面算法，可以解决这个整数线性程序实践中的最优性。通过对标准 Reactome 和 NCI-PID 反应数据库中数千个实例的综合实验，我们证明了我们的切割平面算法可以快速找到最佳超路径（推断最可能的路径），中位运行时间不到 10 秒，并且最长时间少于 30 分钟，即使在有数千个反应的情况下也是如此。我们还首次探索了超路径推断真实路径的效果，并表明最短超路径能够准确地恢复已知路径，通常具有非常高的精度和召回率。实现我们的最短超路径切割平面算法的源代码可免费用于名为 Mmunin 的新工具中的研究使用。