Abstract
The evolutionary origin of universal statistics in biochemical reaction networks is studied, to explain the power-law distribution of reaction links and the power-law distributions of chemical abundances. Using cell models with catalytic reaction networks, we confirmed that the power-law distribution in abundances of chemicals emerges by the selection of cells with higher growth speeds, as suggested in our previous study. Through the further evolution, this inhomogeneity in chemical abundances is shown to be embedded in the distribution of links, leading to the power-law distribution. These findings provide novel insights into the nature of network evolution in living cells.
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The rank distribution, i.e., the abundances x plotted by rank n can be transformed to the density distribution p(x), the probability that the abundance is between x and x + dx. Since dx = dx/dn×dn , there are |dx/dn|− 1 chemical species between x and x + dx. Thus, if the abundance-rank relation is given by a power-law with exponent -1, p(x) = |dx/dn|− 1 ∝ n 2 ∝ x − 2.
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© 2006 Springer-Verlag Berlin Heidelberg
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Furusawa, C., Kaneko, K. (2006). Emergence of Two Power-Laws in Evolution of Biochemical Network; Embedding Abundance Distribution into Topology. In: Ijspeert, A.J., Masuzawa, T., Kusumoto, S. (eds) Biologically Inspired Approaches to Advanced Information Technology. BioADIT 2006. Lecture Notes in Computer Science, vol 3853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11613022_9
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DOI: https://doi.org/10.1007/11613022_9
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