The E. coli transcriptional regulatory network and its spatial embedding.

Usually complex networks are studied as graphs consisting of nodes whose spatial arrangement is of no significance. Several real biological networks are, however, embedded in space. In this paper we study the transcription regulatory network (TRN) of E. coli as a spatially embedded network. The embedding space of this network is the circular E. coli chromosome, i.e. it is practically one dimensional. However, the TRN itself is a high-dimensional network due to the existence of an adequate number of long-range connections. We find that nodes in short topological distance l = 1, 2 tend, on average, to be in shorter spatial distances r indicating an abundance of short-range connections as well. Community analysis of the TRN reveals the interesting fact that highly interconnected subnets consist of nodes that tend to be in spatial proximity on the circular chromosome. We also find indications that for certain transcriptional aspects of the E. coli it is advantageous to treat the circular genome as two line segments starting from the OriC and ending to Ter.