Classification of biological organisms is of fundamental importance to evolutionary studies. It is commonly believed that there are three domains of life: Archaea, Bacteria and Eukaryote. Currently, the most popular classification method is the so called "molecular approach", in which polymorphism information in DNA or protein sequence is exploited to assess the phylogenetic relationships among species 12. To a large extent, this is a "local" approach since the choice of sequence for comparison greatly affects the final result, "lateral gene transfer" (LGT) and thus the resulting "genome chimerism" further complicates the situation 3. A new "system" approach that takes "global" properties of each organism into consideration serves as a potential alternative to overcome this shortcoming. Indeed, recent advances in system biology and increasingly available genomic databases have made it possible to rebuild biological networks from genomic data and have offered opportunity for such a "system" approach 4.

Podani and co-workers 5 proposed classifying organisms based on two kinds of network indices: the Jaccard index, which measures proportions of common sets of nodes in two networks, and Goodman-Kruskal γ function, which measures the similarity between rankings of nodes in two networks. They studied metabolic and information network structures of 43 organisms using these two measures under the hypothesis that network structure and the network design principle(s) behind them contain phylogenetic information. Ma and Zeng 6 conducted a more extensive phylogenetic classification study on 82 fully sequenced organisms based on different cellular function systems (enzyme, reaction, and genes) at the genomic level. They constructed phylogenetic tree based on Jaccard index and Korbel's definition, and concluded that in general, the classification based on network indices are in good agreement with the one obtained by analyzing the 16S rRNA using molecular approach. These studies seem to support the notion that significant differences in the network design principle(s) exist among the three domains of life 7. These differences may reflect on the different approaches that organisms take to organize their entire systems to serve their special needs in the environment they live during the evolutionary history. Motivated by these encouraging results, in this manuscript, we went on to conduct a thorough comparison of network structural properties which provide further and more compelling evidences that significant differences exist among the network design principle(s) in organisms from the three domains of life.

Restricted by the theoretical network structural studies, there are not many deterministic and informative topological measurements available 891011. The established measurements can be roughly divided into two categories: higher-level (global) properties and low-level (local) properties. The difference between the two is that one needs to know the whole network in order to calculate the higher-level property measures (e.g. average path length) while the low-level properties can be worked out locally (e.g. marginal degree of individual node) 9. We use three groups of topological measurements (both low and higher-level) that address different aspects of the network structure. The first group contains network indices such as average clustering coefficient, average path length 12. The second group is composed of degree distributions (both marginal and bivariate joint degree distributions) 89101113. The third group is composed of network motif profiles that are recently shown to represent the network design principle(s) and global statistical properties of the network when aggregating together 141516. These measurements have been well studied in the network literatures, and are able to capture most aspects of network degree information.

Single cell model organisms such as E. coli and S. cerevisiae have been studied intensively in biochemistry, cell biology and genetics; hence the rebuilt networks in those organisms present the best chance to approximate the true underlying network. Moreover, single cell organisms are less likely to have experienced the Whole Genome Duplication (WGD), which might drastically change the network structure 1718. As a result, we selected eleven single cell organisms to study their network structural properties: one Eukaryote: S. cerevisiae; six Bacteria: E. coli, V. cholerae, R. solanacearum, B. subtilis, L. lactis, S. coelicolor; and four Archaea: S. solfataricus, S. tokodaii, M. acetivorans, T. acidophilum.

There are three main types of intracellular networks: the protein-protein interaction network, the transcriptional regulation network and the metabolic network. The first two are rebuilt by using high throughput techniques such as yeast two-hybrid system, in vivo pull down assay or DNA microarray, which are subject to high uncertainties, and the resulting networks may not be good approximation to biological complexity 19202122. On the other hand, the metabolic network is derived from metabolic pathways, many of which are inferred from biochemical experiment-defined stoichiometries of many reactions 23. It is well known that central pathways contain "hub nodes" of the whole metabolic network 2425 and are also main building blocks of the so-called Giant Strongly Connected Component (GSCC) and Giant Weakly Connected Components (GWCC) 26. The former is defined as the largest cluster of nodes within which any pair of nodes is mutually reachable from each other, and the latter is defined as the largest cluster of nodes within which each pair of nodes is connected in the underlying undirected graph 10. Therefore, our high confidence in the structure of GSCC and GWCC, based on experimentally verified pathways, guarantees high confidence in whole network structure. The long history of biochemical studies of enzymes ensures relatively low false positive and low false negative rates of connections. Therefore, we decided to use metabolic networks in single cell organisms to compare network topological properties in the three domains of life.

In constructing metabolic networks, Ma and Zeng 28 argued that connections through "current metabolites", which is referred to as cofactors in biochemistry such as ATP, ADP, H₂O, should be removed from metabolic networks. We followed their suggestions by removing such "current metabolites" before conducting the following analysis.

Based on our comparison of network structural properties beyond network indices, we were able to gain more insight into the structural differences across the three domains of life. Having shown that the metabolic network is "scale-free", we further showed that metabolic networks in the four Archaeal species are closer to "exponential random network" [9:Ch2, 11] than those in S. cerevisiae and the six Bacterial species. The reasons are the following:

First, the Archaeal metabolic networks are visually more homogeneous among themselves compared to their counterparts in the non-Archaeal species. In random networks, any pair of nodes is equally likely to be connected. The network topology should look homogeneous given that the size of network is large enough. The "scale-free" network, on the other hand, features a highly modular and heterogeneous topology since the marginal degree is power-law distributed 89. Moreover, the marginal degree distributions of the metabolic networks in non-Archaeal species fit the power-law model better than Archaeal species (Table 2 and Table 3).

Second, the average clustering coefficient and average betweenness of Archaeal metabolic networks are much smaller than those in S. cerevisiae and the six Bacterial species. The same is true for the concentrations of three-node and four-node subgraphs. As pointed out by Watts and Strogatz, real-life networks show strong clustering or network transitivity while exponential random network does not 12.

Third, there is no three-node motif and fewer four-node motifs found in Archaeal metabolic networks compared to non-Archaeal metabolic networks. In particular, the ubiquitous feed-forward loop (FFL) motif found in networks from biology (including metabolic networks in S. cerevisiae and the six Bacteria species in this study) to neurology and engineering fields was not found in any of the four Archaeal metabolic networks (Fig. 6). Since motifs are statistically significant subgraphs compared to "properly" randomized network ensembles, no motif or fewer than usual motifs found in a real-life network indicates that the network structure is closer to that of a random network. It has been shown by Milo et al. 15 that concentration of FFL motif is insensitive to the network size within E. coli transcription regulation network, but diminishes to zero in increasingly larger random networks. This also supports that Archaeal metabolic networks are closer to randomized network ensembles than other real-life networks.

The metabolic networks in Archaea are both "random-like" and "scale-free", which might exert profound influences on their adaptability to the hostile environment. Archaeal species are typically restricted to marginal habitats such as hot springs or areas of low oxygen concentration and can assimilate different kinds of inorganic carbon and nitrogen sources. Indeed, the chemical structure and component of the macromolecules such as protein and lipid make significant contributions to the organism's adaptability to the environment. The seemingly ad hoc network organization (both "random-like" and "scale-free") in Archaeal species might also enabled them to survive in those extreme physiological conditions. Archaeal species might employ some biologically significant subgraphs (rather than statistically significant motifs) which can not be detected by current motif searching algorithm 15. This makes the Archaeal metabolic networks appear random in statistical sense (not statistically significantly different from random networks) but not in biological sense.

Our comparison results showed that many network structural properties measured in Archaeal species are different from those of non-Archaeal species. However, the hidden anthropomorphic factors might account for some of the differences observed. Specifically, the drastic differences of topological profiles between the metabolic networks of Archaeal species and non-Archaeal species may be partially explained by the fact that significantly less extensive metabolic pathway studies have been conducted in Archaeal species 32. Robustness of topological profiles against random perturbations can alleviate the impact to a certain extent but is unable to eradicate it 9.

Our network analysis results showed that in most of higher-level (global) topological properties measured, metabolic networks in the four Archaeal species are similar to each other but significantly different from those in S. cerevisiae and the six Bacterial species. This provides further evidence that the metabolic network structures and consequently the design principle(s) in the four Archaeal species are very different from those in S. cerevisiae (Eukaryote) and the six Bacterial species. Our finding that the metabolic networks in Archaeal species possess many properties of the exponential random network begs for better understanding of the design principle(s) in biological networks, which may be revealed by further systematic analyses. For example, locate and align conservative pathways such as glycosis between E. coli or S. cerevisiae and Archaeal species to understand the functional mechanisms of Archaeal metabolic networks.

DZ and ZSQ conceived and designed the study; DZ wrote the computer code, analyzed the data and draft the manuscript. Both authors read and approved the final manuscript.