The Blind Watchmaker Network: Scale-Freeness and Evolution Petter Minnhagen1,2, Sebastian Bernhardsson1,2* 1 Department of Theoretical Physics, Umea˚ University, Umea˚, Sweden, 2 Center for Models of Life, Copenhagen, Denmark Abstract It is suggested that the degree distribution for networks of the cell-metabolism for simple organisms reflects a ubiquitous randomness. This implies that natural selection has exerted no or very little pressure on the network degree distribution during evolution. The corresponding random network, here termed the blind watchmaker network has a power-law degree distribution with an exponent c$2. It is random with respect to a complete set of network states characterized by a description of which links are attached to a node as well as a time-ordering of these links. No a priory assumption of any growth mechanism or evolution process is made. It is found that the degree distribution of the blind watchmaker network agrees very precisely with that of the metabolic networks. This implies that the evolutionary pathway of the cell- metabolism, when projected onto a metabolic network representation, has remained statistically random with respect to a complete set of network states. This suggests that even a biological system, which due to natural selection has developed an enormous specificity like the cellular metabolism, nevertheless can, at the same time, display well defined characteristics emanating from the ubiquitous inherent random element of Darwinian evolution. The fact that also completely random networks may have scale-free node distributions gives a new perspective on the origin of scale-free networks in general. Citation: Minnhagen P, Bernhardsson S (2008) The Blind Watchmaker Network: Scale-Freeness and Evolution. PLoS ONE 3(2): e1690. doi:10.1371/ journal.pone.0001690 Editor: Ji Zhu, University of Michigan, United States of America Received November 13, 2007; Accepted January 27, 2008; Published February 27, 2008 Copyright: 2008 Minnhagen, Bernhardsson. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported by the Swedish Research Council through contract 50412501. Competing Interests: The authors have declared that no competing interests exist. * E-mail: sebbeb@tp.umu.se Introduction A network is a representation of who or what is connected to, or influenced by, whom or what. To characterize the structure of a network, researchers often measure its degree distribution N(k), the number of nodes with k links attached. Numerous studies have found that real-world networks often have very broad degree distributions for larger k, N(k),k2c; These fat tailed distributions approximate a power law in their structure [1][2][3][4][5]. They are also called scale-free networks because a power-law tail indicates the lack of an intrinsic characteristic degree size. Biological networks are particu- larly interesting because the structure of these networks have, directly or indirectly, arisen through the process of evolution by natural selection. These networks have been constructed as if by a blind watchmaker, through the interplay between a random stochastic evolution and a natural selection process [6]. So what can we learn from the observation that a biological network such as the network of the metabolism of a cell has a power law distribution [7]? In order to answer this question we define and investigate a blind watchmaker network. We demonstrate that the empirically observed degree distributions for networks of the cellular metabolism for simple organisms are good approximations of this random structure. Previous authors have ascribed the scale-free structure of biological networks to various aspects of the evolutionary process: Either the scale-free network structure has been suggested to confer an evolutionary advantage[8][9], or the elementary mechanism for growth of the network has been suggested to generate a priori a scale- free network [10][11][12][13]. Our findings are to the contrary: The close correspondence between the blind watchmaker network and the structure of empirical networks implies that the evolutionary pathway leading to the construction of the cell-metabolism, when projected onto our network representation, is statistically random with respect to a complete set of network states (see Figs. 1 and 2). Thus our findings provide a new perspective on the origin of scale- free network structures [1][2][3][4][5]. The cells living today have evolved into their present forms during some 46109 years. An important part of the cell is its metabolism which provides the cell with substances necessary for sustaining life. It is a chemical mini-factory usually involving of the order of 500 to 1000 substances in a complex network of metabolic reactions. Some substances like water and NAD+ take part in very many chemical reactions producing new substances either needed in the chemical mini-factory itself to produce other substances, or needed in some other function in the cell, or in fact both [14][15]. Other substances like iron are just needed for some specific purpose in the cell. One possible metabolic network representation is constructed as follows: Substrates and products in the cell metabolism are nodes. Two nodes are connected if the substance of one is a substrate in a metabolic reaction which produces the substance represented by the other node. This means that each node corresponds to a particular substance and that the links denote its connections to other substances. One characteristic feature of a network is its degree distribution N(k). In the present context this is the number of substances which are connected to precisely k other substances. Figure 3(b) shows the degree distribution for the metabolic network of the E. Coli. bacteria. Here the substance with the most connection is water with 302 connections followed by NAD+ with 141 connections. In Fig. 3(b) these two substances corresponds to PLoS ONE | www.plosone.org 1 February 2008 | Volume 3 | Issue 2 | e1690