Investigations into the relationship between feedback loops and functional importance of a signal transduction network based on Boolean network modeling

Abstract

Background: A number of studies on biological networks have been carried out to unravel the topological characteristics that can explain the functional importance of network nodes. For instance, connectivity, clustering coefficient, and shortest path length were previously proposed for this purpose. However, there is still a pressing need to investigate another topological measure that can better describe the functional importance of network nodes. In this respect, we considered a feedback loop which is ubiquitously found in various biological networks. Results: We discovered that the number of feedback loops (NuFBL) is a crucial measure for evaluating the importance of a network node and verified this through a signal transduction network in the hippocampal CAI neuron of mice as well as through generalized biological network models represented by Boolean networks. In particular, we observed that the proteins with a larger NuFBL are more likely to be essential and to evolve slowly in the hippocampal CAI neuronal signal transduction network. Then, from extensive simulations based on the Boolean network models, we proved that a network node with the larger NuFBL is likely to be more important as the mutations of the initial state or the update rule of such a node made the network converge to a different attractor. These results led us to infer that such a strong positive correlation between the NuFBL and the importance of a network node might be an intrinsic principle of biological networks in view of network dynamics. Conclusion: The presented analysis on topological characteristics of biological networks showed that the number of feedback loops is positively correlated with the functional importance of network nodes. This result also suggests the existence of unknown feedback loops around functionally important nodes in biological networks.