Protein–protein interaction network of E. coli K‐12 has significant high‐dimensional cavities: new insights from algebraic topological studies

As a model system, Escherichia coli has been used to study various life processes. A dramatic paradigm shift has occurred in recent years, with the study of single proteins moving toward the study of dynamically interacting proteins, especially protein–protein interaction (PPI) networks. However, despite the importance of PPI networks, little is known about the intrinsic nature of the network structure, especially high‐dimensional topological properties. By introducing general hypergeometric distribution, we reconstruct a statistically reliable combined PPI network of E. coli (E. coli‐PPI‐Network) from several datasets. Unlike traditional graph analysis, algebraic topology was introduced to analyze the topological structures of the E. coli‐PPI‐Network, including high‐dimensional cavities and cycles. Random networks with the same node and edge number (RandomNet) or scale‐free networks with the same degree distribution (RandomNet‐SameDD) were produced as controls. We discovered that the E. coli‐PPI‐Network had special algebraic typological structures, exhibiting more high‐dimensional cavities and cycles, compared to RandomNets or, importantly, RandomNet‐SameDD. Based on these results, we defined degree of involved q‐dimensional cycles of proteins (q‐DC(protein)) in the network, a novel concept that relies on the integral structure of the network and is different from traditional node degree or hubs. Finally, top proteins ranked by their 1‐DC(protein) were identified (such as gmhB, rpoA, rplB, rpsF and yfgB). In conclusion, by introducing mathematical and computer technologies, we discovered novel algebraic topological properties of the E. coli‐PPI‐Network, which has special high‐dimensional cavities and cycles, and thereby revealed certain intrinsic rules of information flow underlining bacteria biology.