The study of the scale-free topology in non-biological and biological networks and the dynamics that can explain this fascinating property of complex systems have captured the attention of the scientific community in the last years. Here, we analyze the biochemical pathways of three organisms (Methanococcus jannaschii, Escherichia coli, Saccharomyces cerevisiae) which are representatives of the main kingdoms Archaea, Bacteria and Eukaryotes during the course of the biological evolution. We can consider two complementary representations of the biochemical pathways: the enzymes network and the chemical compounds network. In this article, we propose a stochastic model that explains that the scale-free topology with exponent in the vicinity of gamma approximately 3/2 found across these three organisms is governed by the log-normal dynamics in the evolution of the enzymes network. Precisely, the fluctuations of the connectivity degree of enzymes in the biochemical pathways between evolutionary distant organisms follow the same conserved dynamical principle, which in the end is the origin of the stationary scale-free distribution observed among species, from Archaea to Eukaryotes. In particular, the log-normal dynamics guarantees the conservation of the scale-free distribution in evolving networks. Furthermore, the log-normal dynamics also gives a possible explanation for the restricted range of observed exponents gamma in the scale-free networks (i.e., gamma > or = 3/2). Finally, our model is also applied to the chemical compounds network of biochemical pathways and the Internet network.
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Evidence ID | Analyze ID | Gene/Complex | Systematic Name/Complex Accession | Qualifier | Gene Ontology Term ID | Gene Ontology Term | Aspect | Annotation Extension | Evidence | Method | Source | Assigned On | Reference |
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Evidence ID | Analyze ID | Gene | Gene Systematic Name | Phenotype | Experiment Type | Experiment Type Category | Mutant Information | Strain Background | Chemical | Details | Reference |
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Evidence ID | Analyze ID | Gene | Gene Systematic Name | Disease Ontology Term | Disease Ontology Term ID | Qualifier | Evidence | Method | Source | Assigned On | Reference |
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Evidence ID | Analyze ID | Regulator | Regulator Systematic Name | Target | Target Systematic Name | Direction | Regulation of | Happens During | Regulator Type | Direction | Regulation Of | Happens During | Method | Evidence | Strain Background | Reference |
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Site | Modification | Modifier | Source | Reference |
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Evidence ID | Analyze ID | Interactor | Interactor Systematic Name | Interactor | Interactor Systematic Name | Allele | Assay | Annotation | Action | Phenotype | SGA score | P-value | Source | Reference | Note |
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Evidence ID | Analyze ID | Interactor | Interactor Systematic Name | Interactor | Interactor Systematic Name | Assay | Annotation | Action | Modification | Source | Reference | Note |
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Complement ID | Locus ID | Gene | Species | Gene ID | Strain background | Direction | Details | Source | Reference |
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Evidence ID | Analyze ID | Dataset | Description | Keywords | Number of Conditions | Reference |
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