Long-range correlations in the phase-shifts of numerical simulations of biochemical oscillations and in experimental cardiac rhythms

Journal of Biological Systems

Volumn 7, Issue 2, 1999, Pages 113-130

  De La Fuente, I M ^a   Martinez, L ^a   Aguirregabiria, J M ^a   Veguillas, J ^a   Iriarte, M ^b  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b HOSPITAL DE BASURTO   (Spain)

Author keywords

Biological rhythms; Cell behavior; Dissipative structures; Fractals; Oscillatory enzymes

Indexed keywords

EID: 0042229339     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339099000103     Document Type: Article

References (42)

1. Alkon L. D. and Rasmussen H., A spatial-temporal model of cell activation, Nature 239 (1988) pp. 998-1004.
2. Anderson C. M, Mandell A. J. and Selz K. A., The development of nuchal atonia associated with active (REM) sleep in fetal sheep: presence of recurrent fractal organization, Brain Res. 787 (1988) pp. 351-357.
3. Barnsley M. F. and Sloan A. D., A better way to compress images, Byte 13 (1988) pp. 215-223.
4. Bashir Z. I., Induction of LTP in the hippocampus needs, Nature 363 (1993) pp. 347-350.
5. Betz A. and Chance B., Phase relationship of glycolytic intermediates in yeast cells and with oscillatory metabolic control, Arch. Biochem. Biophys. 109 (1965) pp. 585-594.
6. Canessa E. and Calmetta A., Physics of a random biological process, Phys. Rev. E50 (1994) pp. R47-R49.
7. Decroly O. and Goldbeter A., Birhythmicity, chaos and other patterns of temporal self-organization in a multiply regulated biochemical system, Proc. Natl. Acad. Sci. USA 79 (1982) pp. 6917-6921.
8. De la Fuente M. I., Martínez L. and Veguillas J., Dynamic behavior in glycolytic oscillations with phase-shifts, Biosystems 35 (1995) pp. 1-13.
9. De la Fuente M. I., Martínez L., Veguillas J. and Aguirregabiria J. M., Quasiperiodicity route to chaos in a biochemical system, Biophys. J. 71 (1996) pp. 2375-2379.
10. De la Fuente M. I., Martínez L. and Veguillas J., Intermittency route to chaos in a biochemical system, Biosystems 39 (1996b) pp. 87-92.
11. De la Fuente M. I., Martínez L., Veguillas J. and Aguirregabiria J. M., Coexistence of multiple periodic and chaotic regimes in biochemical oscillations, Acta Biotheoretic. 46 (1998a) pp. 37-51.
12. De la Fuente M. I., Martínez L., Aguirregabiria J. M. and Veguillas J., R/S analysis in strange attractors, Fractals 6 (1998b) pp. 95-100.
13. De la Fuente M. I., Martínez L., Benitez N., Veguillas J. and Aguirregabiria J. M., Persistent behavior in a phase-shift sequence of periodical biochemical oscillations, Bull. Math. Biol. (1998c) in press.
14. Eduarws A. F., LTP - a structural model to explain the inconsistencies, TINS 18 (1995) pp. 250-255.
15. Edmunds L. N., Cell Cycle Cloks (Marcel Dekker, New York, 1984).
16. Feder J., Fractals (Plenum, New York, 1990).
17. Frenkel R., Control of reduced diphosphopyridine nucleotide oscillations in beef heart extracts, Arch. Biochem. Biophys. 125 (1968) pp. 157-165.
18. Glass L. and M. Mackey, From Clocks to Chaos (Mir, Moscow, 1991).
19. Goldbeter A., Rythmes et Chaos dans les Systémes Biochémiques et Cellulaires (Masson, Paris, 1990).
20. Greenberg S. M., Castelluccci V. F., Hawkins R. D. and Kandell E. R., A molecular mechanism for long-term sensitization in Aplysia, Nature 329 (1987) pp. 62-65.
21. Hess B. and Boiteux A., Control of glycolysis, Regulatory Functions of Biological Membranes (Elsevier, Amsterdam, 1968).
22. Hess B., Kuschmitz D. and Markus M., Dynamics of Biochemical Systems, ed. by Ricard J. and Cornish-Bowden A. (Plenum, New York, 1984).
23. Hurst H. E., Black R. P. and Simaika Y. M., Long-Term Storage: An Experimental Study (Constable, London, 1965).
24. Kandel R. E., Schwartz H. J. and Jessell M. T., Principles of Neural Science (Prentice-Hall, Toronto, 1991).
25. Li Y. X. and Goldbeter A., Oscillatory isozymes as the simplest model for coupled biochemical oscillators, J. Theor. Biol. 138 (1989) pp. 149-174.
26. Mandelbrot B. B. and Walis J. R., Noah, Joseph, and operational hydrology, Water Resour. Res. 4 (1968) pp. 909-918.
27. Mandelbrot B. B. and Walis J. R., Some longe run properties of geophysical records, Water Resour. Res. 5 (1969a) pp. 321-340.
28. Mandelbrot B. B. and Walis J. R., Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence, Water Resour. Res. 6 (1969b) pp. 967-988.
29. Mandelbrot B. B., Statistical methodology for non-periodic cycles: from the covarianze to R/S analysis, Annals of Economic and Social Measurement 1 (1972).
30. Mandelbrot B. B., Self-affine fractals and fractal dimension, Phys. Scr. 32 (1985) pp. 257-260.
31. Mandelbrot B. B., Self-affine fractal sets, in Fractals in Physics, ed. by L. Pietronero and E. Tossatti (North-Holland, Amsterdam, 1986).
32. McMurry L. and Hastings J. W., No desynchronization among four different circadian rhythms in the unicellular alga, Euglena gracilis, Science 175 (1972) pp. 1137-1139.
33. Nicolis G. and Prigogine I., Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order Through Fluctuations (Wiley, New York, 1977).
34. Peters E., Chaos and Order in the Capital Markets (Wiley, New York, 1991).
35. Peng C. K., Buldyrev S. V., Goldberger A. L., Havlin S., Sciortino F., Simons M. and Stanley H. E., Long-range correlations in nucleotide sequences, Nature 366 (1992) pp. 168-170.
36. Peng C. K., Mietus J., Hausdorff J. M., Havlin S., Stanley H. E. and Goldberger A. L., Long-range anticorrelations and non-gaussian behavior of the heartbeat, Phys. Rev. Lett. 70 (1993) pp. 1343-1346.
37. Pye E. K., Biochemical mechanisms underlying the metabolic oscillations in yeast, Can. J. Bot. 47 (1969) pp. 271-285.
38. Viswanathan G. M., Buldyrev S. V., Havlin S. and Stanley H. E., Quantification of DNA patchiness using long-range correlation measures, Biophys. J. 73 (1997) pp. 2848-2849.
39. Voss R. F., Random fractal forgeries, in Fundamental Algorithms in Computer Graphics, ed. by R. A. Earnshaw (Springer-Verlag, Berlin, 1985).
40. Voss R. F., Evolution of log-range fractal correlations and 1/f noise in DNA base sequences, Phys. Rev. Lett. 68 (1992) pp. 3805-3808.
41. Winfree A. T., The Geometry of Biological Time (Springer, New York, 1980).
42. Winn K., Addition and subtraction by human infants, Nature 358 (1992) pp. 749-750.