Hypoxia Regulated Gene Network in Glioblastoma Has Special Algebraic Topology Structures and Revealed Communications Involving Warburg Effect and Immune Regulation.

Hypoxia regulated genes (HRGs) formed a complex molecular interaction network (MINW), contributing to many aspects of glioblastoma (GBM) tumor biology. However, little is known about the intrinsic structures of the HRGs-MINW, mainly due to a lack of analysis tools to decipher MINWs. By introducing general hyper-geometric distribution, we obtained a statistically reliable gene set of HRGs (SR-HRGs) from several datasets. Next, MINWs were reconstructed from several independent GBM expression datasets. Algebraic topological analysis was performed to quantitatively analyze the amount of equivalence classes of cycles in various dimensions by calculating the Betti numbers. Persistent homology analysis of a filtration of growing networks was further performed to examine robust topological structures in the network by investigating the Betti curves, life length of the cycles. Random networks with the same number of node and edge and degree distribution were produced as controls. As a result, GBM-HRGs-MINWs reconstructed from different datasets exhibited great consistent Betti curves to each other, which were significantly different from that of random networks. Furthermore, HRGs-MINWs reconstructed from normal brain expression datasets exhibited topological structures significantly different from that of GBM-HRGs-MINWs. Analysis of cycles in GBM-HRGs-MINWs revealed genes that had clinical implications, and key parts of the cycles were also identified in reconstructed protein-protein interaction networks. In addition, the cycles are composed by genes involved in the Warburg effect, immune regulation, and angiogenesis. In summary, GBM-HRGs-MINWs contained abundant molecular interacting cycles in different dimensions, which are composed by genes involved in multiple programs essential for the tumorigenesis of GBM, revealing novel interaction diagrams in GBM and providing novel potential therapeutic targets.