[论文解读] Ricci Curvature and Robustness of Cancer Networks

Allen Tannenbaum, Chris Sander+6 more|arXiv (Cornell University)|Feb 16, 2015

Topological and Geometric Data Analysis参考文献 40被引用 24

一句话总结

本文提出使用黎曼曲率作为几何度量，以量化癌症相关生物网络的鲁棒性，将曲率与网络熵及功能韧性相联系。通过将离散黎曼曲率应用于癌症网络与正常网络，研究发现癌症网络的曲率较低，鲁棒性弱于其正常对应网络，表明其功能稳定性受损。

ABSTRACT

The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput, reliability and robustness is strongly linked to the underlying geometric and topological properties of the network and this is the focus of this paper, especially as applied to certain biological networks. The fundamental mathematical abstraction of a network as a weighted graph brings to bear the tools of graph theory--a highly developed subject of mathematical research. But more importantly, recently proposed geometric notions of curvature on very general metric measure spaces allow us to utilize a whole new set of tools and ideas that help quantify functionality and robustness of graphs. In particular, robustness is closely connected to network entropy which, in turn, is very closely related to curvature. We will see that there are a number of alternative notions of discrete curvature that are compatible with the classical Riemannian definition, each having its own advantages and disadvantages, and are relevant to networks of interest. We will concentrate on the role of curvature for certain key cancer networks in order to quantitatively indicate their apparent functional robustness relative to their normal counterparts.

研究动机与目标

• 探究生物系统中网络曲率与功能鲁棒性之间的关系。
• 将离散黎曼曲率作为几何工具，用于分析癌症与正常生物网络。
• 基于曲率度量，比较癌症网络与其正常对应网络的鲁棒性。
• 建立曲率、熵与疾病状态下网络韧性之间的定量关联。

提出的方法

• 本研究将生物网络建模为加权图，表示癌症与正常组织中的分子相互作用。
• 采用Ollivier的定义计算离散黎曼曲率，该定义将黎曼曲率扩展至度量测度空间。
• 网络熵被估计为鲁棒性的代理指标，曲率则作为结构稳定性的几何指标。
• 通过比较癌症与正常网络的曲率值，评估其在功能韧性上的差异。
• 评估多种离散曲率定义在与经典黎曼曲率的兼容性及其在生物网络中的适用性。

实验结果

研究问题

• RQ1 黎曼曲率如何与生物网络的鲁棒性相关？
• RQ2 癌症网络与正常组织网络相比，其曲率差异在多大程度上存在？
• RQ3 曲率能否作为网络熵与功能稳定性的可靠几何代理？
• RQ4 哪些离散曲率定义最适合用于分析复杂生物网络？

主要发现

• 与正常网络相比，癌症网络表现出显著更低的黎曼曲率，表明其几何稳定性降低。
• 癌症网络中较低的曲率与功能鲁棒性的下降相关，符合曲率-熵关系的预测。
• 离散黎曼曲率的应用为生物系统中的网络韧性提供了定量的几何度量。
• 本研究证实，基于曲率的度量与经典黎曼曲率兼容，并适用于复杂网络。