Scaling theory of transport in complex biological networks.

Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well understood in these systems, probably because of the lack of a general theoretical framework. Here, based on the finding that renormalization can be applied to bionetworks, we develop a scaling theory of transport in self-similar networks. We demonstrate the networks invariance under length scale renormalization, and we show that the problem of transport can be characterized in terms of a set of critical exponents. The scaling theory allows us to determine the influence of the modular structure on transport in metabolic and protein-interaction networks. We also generalize our theory by presenting and verifying scaling arguments for the dependence of transport on microscopic features, such as the degree of the nodes and the distance between them. Using transport concepts such as diffusion and resistance, we exploit this invariance, and we are able to explain, based on the topology of the network, recent experimental results on the broad flow distribution in metabolic networks.