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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Furusawa, C., Kaneko, K.: Zipf’s Law in Gene Expression. Phys. Rev. Lett. 90, 88102 (2003)
Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., Barabási, A.-L.: The large-scale organization of metabolic networks. Nature 407, 651 (2000)
Jeong, H., Mason, S.P., Barabási, A.-L.: Lethality and centrality in protein networks. Nature 411, 41 (2001)
Li, S., et al.: A map of the interactome network of the metazoan C. elegans. Science 303, 540 (2004)
Featherstone, D.E., Broadie, K.: Wrestling with pleiotropy: genomic and topological analysis of the yeast gene expression network. Bioessays 24(3), 267–74 (2002)
Guelzim, N., Bottani, S., Bourgine, P., Kepes, F.: Topological and causal structure of the yeast transcriptional regulatory network. Nature Genet. 31, 60 (2002)
Ueda, H.R., et al.: Universality and flexibility in gene expression from bacteria to human. Proc. Natl Acad. Sci. USA 101, 3765 (2003)
Kuznetsov, V.A., et al.: Genetics 161, 1321 (2002)
Almaas, E., et al.: Nature 427, 839 (2004)
We confirmed that our results are qualitatively same when we use distributed reaction coefficients for the simulations
Kaneko, K., Yomo, T.: Jour. Theor. Biol. 199, 243 (1999)
Furusawa, C., Kaneko, K.: Phys. Rev. Lett. 84, 6130 (2000)
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.
As for the number distribution of reaction links, the simulation has not yet reached the stage to show the scale-free statistics in a network clearly (since the simulation requires much longer time than the present method), but still we found that the number distribution of such network show heterogeneity in number of reaction links, with significant deviation from those of random networks
Barabási, A.-L., Albert, R.: Science 286, 509 (1999)
Barrat, A., Barthélemy, M., Vespignani, A.: Phys. Rev. Lett. 92, 228701 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/11613022_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31253-6
Online ISBN: 978-3-540-32438-6
eBook Packages: Computer ScienceComputer Science (R0)