and 3(d) these networks are compared to the corresponding blind watchmaker network: the only information contained in this latter network is the number of nodes and links and the number of networks involved in the average. We again stress that both the shape of the distribution and the spread of the data are important characteristics of a real network. As apparent from Fig. 3(c) the overlap between the two data-sets is striking. From this we conclude that metabolic networks are to large extent blind watchmaker networks. Figure 3(d) compare a single metabolic network (E. Coli.) with the corresponding random network. A particular feature in this comparison is the large split off nodes. In case of E. Coli. there are 6 nodes with more than 100 links and for the corresponding blind watchmaker there are on the average 5.361.5. Even if the blind watchmaker network explains the overall feature such as the fat tails of biological networks like the metabolic ones, there are of course differences. One such difference is the low number of nodes with only one link in case of metabolic networks. Such systematic deviations signal additional constraints in the real network. Whenever such constraints are present the entropy of the distribution is lower than for the blind watchmaker network. To illustrate this we in Fig. 3(e) and 3(f) compare the real networks with the corresponding blind watchmaker network including the least biased constraint which adjusts the number of single-link nodes (details in Supporting Information Text S1). Now the agreement is extraordinary considering the fact that only one data point, the number of single-link nodes at the very beginning of the distribution, has been adjusted. It clearly demonstrates that it is rather the deviations from the blind watchmaker network which needs to be explained (like in the present case the smaller number of single -link nodes): These deviations contain information about the system in addition to the less system specific information represented by the blind watchmaker network. In the present work we focus on the different possible states a network can be found in. These network states distinguishes between the time order in which a node is connected to its neigbours. No a priory assumption of any growth mechanism or evolution process is made. We introduce the concept of random with respect to the network states and call the corresponding network the blind watchmaker network. It is found that the blind watchmaker network is scale-free and that metabolic networks to large extent are blind watchmaker networks. This means that the evolutionary path of the cell-metabolism, when projected onto a metabolic network representation, is statistically random with respect to a complete set of network states. This randomness emanates from the inherent References 1. Albert R, Baraba´si A-L (2002) Statistical mechanics of complex networks. Rev. of Mod. Phys. 74: 47–97. 2. Dorogovtsev SN, Mendes JFF (2003) Evolution of networks: From biological nets to the Internet and WWW. Oxford University Press. 3. Newman MEJ (2003) The structure and function of complex networks. SIAM Review 45: 167–256. 4. Boccaletti S, Latora V, Morena Y, Chavez M, Hwang D-U (2006) Complex networks: Structure and dynamics. Phys. Rep. 424: 175–308. 5. Newman MEJ, Baraba´si A-L, Watts DJ (2006) The Structure and dynamics of networks. Princeton: Princeton University press. 6. Dawkins R (1985) The blind watchmaker: Why the evidence of evolution reveals a universe without design. Norton. 7. Wagner A (2003) Does selection mold molecular networks. Science STKE 41. 8. Albert R, Jeong H, Baraba´si A-L (2000) Error attack and tolerance of complex networks. Nature 406: 378–382. 9. Cohen R, Erez K, ben-Avraham D, Havlin S (2000) Resilience of Internet for random breakdowns. PRL. 85: 4626–4628. 10. Baraba´si A-L, Albert R, Jeong H (1999) Emergence of scaling in complex networks. Science 286: 509–512. 11. Sole´ RV, Pastor-Satorras R, Smith E, Kepler T (2002) A model of large-scale proteomic evolution. Adv. in Complex Systems 5: 43–54. The Blind Watchmaker Network randomness (the blind element) in Darwinian evolution and suggests that natural selection has had no or little effect on the network node degree distribution of metabolic networks. Can these conclusions really be drawn from the agreement between the node degree distribution, the split off nodes and the stochastic spread of the data when comparing the actual data for metabolic networks and the blind watchmaker model network? In our opinion they can be drawn: The key is the quality of the agreement in relation to the number of free adjustable parameters. Earlier attempts to reproduce the degree distribution of metabolic networks usually starts from some assumption about the actual evolutionary path and has to our knowledge not been able to reproduce the data in the way demonstrated here [13]. So why does the evolution of metabolic networks choose this particular stochastic node degree distribution displayed by the blind watchmaker model network? According to us, the answer is that this degree distribution is neutral with respect to natural selection and hence, in this sense, has not been chosen at all. The notion that the node degree distribution for metabolic networks could be neutral with respect to natural selection has also been suggested on the bases of a comparison between the node degree distribution in atmospheric chemical reaction networks (no natural selection) and metabolic networks [20][21]. Materials and Methods The theoretical framework used in the analysis is classical statistical mechanics, both in its conventional variational form described in Text S1 and in its stochastical algorithm form described in Results. The cell- metabolisms data represented by the metabolic networks are taken from Ma and Zeng in Ref. [14] and [15]. Supporting Information at: doi:10.1371/journal.pone.0001690.s001 (0.05 MB Text S1 Found PDF) Author Contributions Conceived and designed the experiments: SB PM. Performed the experiments: SB PM. Analyzed the data: SB PM. Contributed reagents/ materials/analysis tools: SB PM. Wrote the paper: SB PM. 12. Vazquez A, Flammini A, Maritan A, Vespignani A (2003) Modeling of protein interaction networks. Complexus 1: 38–44. 13. Pfeiffer T, Soyer OS, Bonhoeffer S (2005) The evolution of connectivity in metabolic networks. PloS Biology 3: 1269–1275. 14. Ma H, Zeng A-P (2003) Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms. Bioinformatics 19: 270–277. 15. Ma H, Zeng A-P (2003) The connectivity structure, giant strong component and centrality of metabolic networks. Bioinformatics 19: 1423–1430. 16. Jeong H, Tombor B, Albert R, Oltvai ZN, Baraba´si A-L (2000) The large scale organization of metabolic networks. Nature 407: 651–654. 17. Minnhagen P, Bernhardsson S (2007) Optimization and scale-freeness for complex networks. Chaos 17: 0261171–0261177. 18. Jaynes ET (1957) Information theory and statistical mechanics. Phys. Rev. 106: 620–630. 19. Minnhagen P, Bernhardsson S, Kim BJ (2007) Scale-freeness for Networks as a Degenerate Ground State: A Hamiltonian Formulation. EPL 78: 280041– 280045. 20. Wagner A (2005) Robustness and evolvability in living systems. Princeton: Princeton University Press. NJ. 138 p. 21. Gleiss P, Stadler P, Wagner A, Fell D (2001) Relevant cycles in chemical reaction networks. Adv. Complex Systems 4: 207–226. PLoS ONE | www.plosone.org 5 February 2008 | Volume 3 | Issue 2 | e1690