Is scale-free a realistic topology for evolving biochemical networks?

How can a new incoming biochemical node measure the degree of nodes already present in a network and thus decide, on the basis of this counting, to preferentially connect with the more connected ones? Although such explicit comparison and choice is quite plausible in the case of man-made networks, leading the network to a scale-free topology, it is much harder to conceive for biochemical networks such as reaction or protein interaction networks. In this paper, computer experiments of growing networks will be proposed as more elementary but more tractable versions of a long tradition of simulations of immune networks and chemical reaction networks described in past publications and largely forgotten since. These simulations will try to respect as simply and as far as possible basic biochemical characteristics such as the heterogeneity of biochemical nodes, the existence of natural hubs, the way nodes bind by mutual affinity, the significance of type-based networks as compared with instance-based ones and the consequent importance of the nodes concentration to the selection of the partners of the incoming nodes. A scale-free topology will be discussed as a very unlikely outcome when compared with exponential decay obtained by a random growth. We will see that the presence of hubs and all the classical functional properties attributed to them (robustness, small-world and epidemic propagation) might be perfectly compatible with an exponential shape obtained by less constrained growing rules. Initial conceptual issues are first discussed using simplified models and are validated by a more extensive framework based on the logical structure of biochemical systems that was defined for the simulation of dynamics and metadynamics of chemical reaction networks.