Long loops of information flow in genetic networks highlight an inherent directionality

Abstract

Genetic networks integrate the reported interactions between genes into a global view of the transcription regulation. These networks contain, beyond each specific interaction, the information flow between genes and groups of genes that determine the cellular response to different stimuli. The flow of information in such networks is based on the structure of the directed interactions paths, and is not obviously decipherable from the number of paths between genes in the network, which grows exponentially with the number of nodes. We show here that the directional large scale information flow in genetic networks can be understood by combining the cycle (closed walk in graph theory terms) length and distance distributions. These properties are highly sensitive to the effect of flipping the direction of a small number of random edges. Here we focus on cycles composed of back and forth minimal paths between a pair of nodes that we further denote as loops. Intra-cellular networks contain a surprisingly large number of long directed loops that can carry information through multiple components of the network, and in parallel a surprisingly small number of short loops. The direction of practically every edge affects the network’s loop length distribution and the flow of information in the network. Swapping the direction of even 2.5% of the edges in regulatory genetic networks from their target to their source drastically reduces the number of long directed loops. All other properties tested here, such as the clustering coefficient or the degree distributions, are practically not affected by a swap of even 50% of edges. We propose a model of information flow to explain this hyper-sensitivity of the loop length distribution to the direction of edges.