Diffusion limited aggregation and the fractal evolution of gene promoter networks

Gene promoter networks (GPNs) are systems-level representations of the base pair-sharing relationships (graph edges) among promoters (graph nodes). It has been shown in the bacterium E. coli that these networks can contain a fractal nucleus of strong associations suggesting a self-organizing complexity. Here I report results of twenty seven in silico simulations for a diffusion limited aggregation model which accounts for much of the fractal structure previously observed in GPNs. Parameters varied in the model included (a) the frequency of gene duplication events, and the extent of (b) attraction and (c) repulsion presented by the DNAprotein binding chemistry. Both duplication and attraction had significant effects on fractal topology of the GPN nucleus, whereas repulsion due to DNA-protein binding chemistry did not, at least for the levels explored in these simulations. Since repulsion is thought to be a key feature of fractal networks, it is likely that the repulsion in GPNs arises from the sparseness of the promoter space. The generation of a finite random set of promoters leads to sparse occupancy of promoter space which itself presents a considerable repulsion away from the consensus motif, working against the DNA-binding protein's efforts to organize the system of promoters over evolutionary time. This interplay between attractive and repulsive forces in a GPN is sufficient to generate a fractal topology.