Optimal topology of gene-regulatory networks: role of the average shortest path

Gene regulatory networks (GRNs) possess an important structural property; they are sparse and resilient, with a robust topology that affords protection against random "attacks" (e.g., gene deletions). However, such networks exhibit optimal or near-optimal topological features not present in other scale-free networks. This paper utilizes an integer linear program formulation to gauge the exact structural optimality of scale-free networks measured using the average shortest path between transcription factors and the regulated genes of a gene-regulatory network sampled from the Escherichia coli bacterium. While randomly generated versions of these networks show several cases for improvement, few subnetworks sampled from Escherichia coli's transcriptional network show optimized solutions that differ substantially from their original topology. We therefore conclude that sampled transcriptional subnetworks from Escherichia coli exhibit an "optimal" topology not present in alternative networks. Because these analyses do not consider the biology of expression dynamics and are based on topology alone, other communication systems, such as wireless networks, may benefit from a more detailed examination of the role in which the average shortest path affects system function, such as with noise or other signaling disruptions.