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