Abstract
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. 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. 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.
Highlights
The degree of a node is the number of edges that are adjacent to it
The power law (PL) and the generalized power law supplemented with an exponential cut-off (GPL-EC) were widely popularized (Wagner, 2001; Jeong et al, 2001) as the rules describing the distribution of the node degrees in proteinprotein interaction network, attempts at a more exact mathematical description are still being undertaken (Thomas et al, 2003; Berg et al, 2004)
According to the DIP data we could observe that the degree distribution of nodes of S. cerevisiae protein interaction network follows approximately a PL or a GPL-EC, but only for the degree values k smaller than 10
Summary
The degree of a node (or connectivity) is the number of edges that are adjacent to it. The power law (PL) and the generalized power law supplemented with an exponential cut-off (GPL-EC) were widely popularized (Wagner, 2001; Jeong et al, 2001) as the rules describing the distribution of the node degrees in proteinprotein interaction network, attempts at a more exact mathematical description are still being undertaken (Thomas et al, 2003; Berg et al, 2004). The reasons are both of practical and methodological nature. For higher values of k we saw a serious discrepancy between the theory and the experiment, already reported by others as an exponential decay (Wilhelm et al, 2003)
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