Journal de protéomique et bioinformatique
Libre accès

Abstrait

Protein Interaction Network. Double Exponential Model

Piotr H. Pawlowski, Szymon Kaczanowski and Piotr Zielenkiewicz

The proper theoretical description of the distribution of the node degree for yeast protein-protein interaction network was investigated to deal with the observed discrepancy between usually proposed models and the existing data. The power law or the generalized power law with exponential cut-off were shown to be inaccurate within a wide range of degree values. Proposed linear-combination-of-exponentialdecays- method exactly characterizing the distribution by the spectrum of decay constants revealed two separate parameter domains. A consequent hypothesis that the node degree distribution could follow the universal double exponential law was successfully verified by selected model comparison using the AIC criterion. BIND and DIP data for H. pylori, E. coli, S. cerevisiae, D. melanogaster, C. elegans and A. thaliana were used for this purpose. A linear change in the magnitude of the distribution components with proteome size was observed, manifesting the evolutional stability of the process of developing the protein interaction network. Proposed kinetic model of protein evolution, considering the two hypothetical protein classes, first, with a relatively rapid emerging rate and a short characteristic residence time, and the second one, with the opposite properties, analytically described the nature of bi-exponential pattern. The model presents a situation in which evolutionary conserved proteins increase their interactions due to specific kinetic conditions. Thus, we oppose the opinion that the majority of such interactions are biologically significant, and, therefore the older parts of interactome are more complex. We believe that our interactome results support the hypothesis of Stuart Kaufman, presented in his book "The Origin of Order", that random mutations and natural selection constitute the origin of order and complexity.