Abstract
Self-organised critical system might be produced by an auto-regulatory feedback loop between opposite autocatalitic activities of catabolic and anabolic types. This mechanism, named metabolic hypercycle, is described by the Lotka-Volterra prey-predator equation and gives rise to fractal spatiotemporal patterns and rhythms. According to the Zipf’s principle of the least effort, the dynamic stability of the critical states of complex systems is produced by the minimisation of distributions and flows of opposite and correlated processes. Maps and clocks based on metabolic hypercycles might be used by living organisms to maintain their homeodynamic equilibrium and biodiversity at different levels.
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
Gleick J. Chaos, making a new science. Penguin, New York (1987).
Stauffer D., and Stanley H.E. From Newton to Mandelbrot. Springer, New York (1992).
Bak P. How nature works: the science of self-organized criticality. Springer, New York (1996).
Bak P., Tang C., and Wiesenfield K. Self-organized criticality. Physics Review 38: 364–374 (1988).
Binney J.J., Dowrick N.J., Fisher A.J., and Newman M.E.J. The theory of critical phenomena: an introduction to the renormalization group. Oxford Science Publications (1993).
Mandlebrot B.B. The Fractal Geometry of Nature. W.H. Freeman and Co., San Francisco (1983).
Whittaker R.J. 1999. Scaling, energetics and diversity. Nature 401: 865–866 (1999).
Brown J.H., and West G.B. Scaling in Biology. Oxford University Press, New York (2000).
Damiani G. Evolutionary meaning, functions and morphogenesis of branching structures in biology. In: Fractals in biology and medicine (Nonnenmacher T.F., Losa G.A., and Weibel E.R., eds) pp.104–115, Birkhauser-Verlag, Basel (1994).
McMahon T.A., and Bonner J.T. On size and life. Freeman, New York (1983).
West G.B., Brown J.H., and Enquist B.J. A general model for the origin of allometric scaling laws in biology. Science 276: 122–126 (1997).
Enquist B.J., Brown J.H., and West G.B. Allometric scaling of plant energetics and population density. Nature 395:163–165 (1998).
West G.B., Brown J.H., and Enquist B.J. The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 284: 167–169 (1999).
Damiani G Il gioco della vita, la teoria binaria dell’Universo fisico. Editrice Italiana Audiovisivi, Roma (1984).
Damiani G., and Della Franca P. Morphé and Evolution. Biology Forum 90: 227–266 (1997).
Damiani G Evolution of life in a fractal Universe. In: Fractals in biology and medicine Vol. 2 (Losa G.A., Merlini D., Nonnenmacher T.F., and Weibel E.R., eds) pp.169–187, Birkhauser-Verlag, Basel (1998).
Damiani G. Why are fractals everywhere? Chaos, fractals, models (Guineani G., and Salvatori F., eds) pp. 384–390, Italian University Press, Pavia (1998).
Layzer D. The arrow of time. Sci. Am., 233 (6): 56–69 (1975).
Zipf G.K. The human behavior and the principle of least effort. Addison-Wesley Press, Cambridge (1949).
Kauffman S.A. The origins of order. Oxford University Press, New York (1993).
Nicolis G., and Prigogine. Self-Organization in Non-Equilibrium Systems. From Dissipative structures to Order through Fluctuations. Wiley, New York (1977).
Damiani G., and Della Franca P. Transizioni di fase e controllo dei metabolismo. In: La matematizzazione della biologia. Storia e problematiche attuali. (Cerrai P., Freguglia P., eds) pp. 97–106, QuattroVenti, Urbino (1997).
Eigen M., and Schuster P. The Hypercycle. Springer Verlag, Heidelberg (1979).
Szent-Gyorgyi A. Bioelectronics - A study in cellular regulation, defence, and cancer. Academic Press, New York-London (1968).
Yates F.E. Fractal Applications in Biology: Scaling Time in Biochemical Networks. Methods in Enzymology 210: 636–675 (1992).
Jones D.B., Coulson A.F.W., and Duff G.A. Sequence homologies between hsp60 and autoantigens Immunol. Today 14: 115–118 (1993).
Lappé M. The Tao of Immunology. Plenum Publishers, New York (1997).
Ou D., Mitchell L.A., and Tingle A.J. New categorization or HLA DR alleles: a functional basis. Hum. Immunol. 59: 665–676 (1998).
Thaler D. The evolution of genetic intelligence. Science, 264: 224–225 (1994).
Burgos J.D. Fractal representation of the immune B cell repertoire. BioSystems 39: 19–24 (1996).
Burgos J.D., and Moreno-Tovar P. Zipf-scaling behavior in immune system. BioSystems 39: 227–232 (1996).
Russel G.C., Davies C.J., Andersson L., Ellis S.A., Hensen E.J., Lewin H.A., Mikko S., Muggli-Cockett N.E., and van der Poel J.J. (1997) BoLA class II nucleotide. Animal Genet 28: 169–180 (1996).
Solé R.V., Manrubia S.C., Benton M., and Bak P. Self-similarity of extinction statistics in the fossil record. Nature 388: 764–767 (1997).
Harte J., Kinzig A., and Green J. Self-similarity in the distribution and abundance of species. Science 284: 334–336 (1999).
Ritchie M.E. and Olff H.123 Spatial scaling laws yield a synthetic theory of biodiversity Nature 400: 557–560 (1999).
Burlando B. The fractal dimension of taxonomic systems. Journal of Theoretical Biology. 146: 99–114 (1990).
May R.M. The search for patterns in the balance of nature: Advances and retreats. Ecology 67:1115–26 (1986).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Basel AG
About this paper
Cite this paper
Damiani, G. (2002). Metabolic Hypercycles, Universality and Fractals in Biological Evolution. In: Losa, G.A., Merlini, D., Nonnenmacher, T.F., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8119-7_26
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8119-7_26
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9445-6
Online ISBN: 978-3-0348-8119-7
eBook Packages: Springer Book Archive