Fractal topology of gene promoter networks at phase transitions

Abstract

Much is known regarding the structure and logic of genetic regulatory networks. Less understood is the contextual organization of promoter signals used during transcription initiation, the most pivotal stage during gene expression. Here we show that promoter networks organize spontaneously at a dimension between the 1-dimension of the DNA and 3-dimension of the cell. Network methods were used to visualize the global structure of E. coli sigma (σ) recognition footprints using published promoter sequences (RegulonDB). Footprints were rendered as networks with weighted edges representing bp-sharing between promoters (nodes). Serial thresholding revealed phase transitions at positions predicted by percolation theory, and nuclei denoting short steps through promoter space with geometrically constrained linkages. The network nuclei are fractals, a power-law organization not yet described for promoters. Genome-wide promoter abundance also scaled as a power-law. We propose a general model for the development of a fractal nucleus in a transcriptional grammar.

Symmetry in the Language of Gene Expression: A Survey of Gene Promoter Networks in Multiple Bacterial Species and Non-σ Regulons

“…These findings were notable since it is thought that repulsion is a critical causal agent in the development of fractality in most networks [42]. Collectively these patterns supported a weak version of the diffusion limited aggregation model first posed to explain the fractal nuclei in GPNs [36], positing that fractality arises by the random accretion of promoters around the periphery of a GPN, and repulsive forces increase the fractal signal.…”

“…The thresholding of the GPNs at the phase transition (break up of the giant component) revealed nuclei of high-weight edges that represented high bp-sharing among promoters. These GPN nuclei displayed a strong fractal structure [36]. In general, fractal structures display a self-similar symmetry across spatial scales [40], and the presence of a fractal core in the GNP suggested a self-organizing complexity interfacing the evolution of genome regulatory elements and the grammar of transcriptional regulation.…”

“…Base conservation was evaluated using Shannon's information entropy [36] as described for DNA sequences [58,59]:…”

“…Gene Promoter Networks (GPNs)-as opposed to Gene Regulatory Networks (GRNs)-are systems-level representations of the DNA-based language used to initiate gene expression [36]. More literally, a GPN is a network-based rendering of base pair-sharing among the promoter elements within a genome, typically promoters within a regulon.…”

“…GPN analysis was first applied to -factor regulons in the bacterium Escherichia coli [36]. The promoters in these GPNs displayed considerable sequence variation and were not well-represented by a single consensus motif.…”