Ukr.Biochem.J. 2013; Volume 85, Issue 5, Sep-Oct, pp. 191-200

doi: http://dx.doi.org/10.15407/ubj85.05.191

Self-organization and fractality in a metabolic processes of the Krebs cycle

V. I. Grytsay1, I. V. Musatenko2

1Bogolyubov Institute for Theoretical Physics,
National Academy of Sciences of Ukraine, Kyiv;
e-mail: vgrytsay@bitp.kiev.ua;
2Taras Shevchenko National University of Kyiv, Ukraine;
e-mail: ivmusatenko@gmail.com

The metabolic processes of the Krebs cycle is studied with the help of a mathematical model. The autocatalytic processes resulting in both the formation of the self-organization in the Krebs cycle and the appearance of a cyclicity of its dynamics are determined. Some structural-functional connections creating the synchronism of an autoperiodic functioning at the transport in the respiratory chain and the oxidative phosphorylation are investigated. The conditions for breaking the synchronization of processes, increasing the multiplicity of cyclicity, and for the appearance of chaotic modes are analyzed. The phase-parametric diagram of a cascade of bifurcations showing the transition to a chaotic mode by the Feigenbaum scenario is obtained. The fractal nature of the revealed cascade of bifurcations is demonstrated. The strange attractors formed as a result of the folding are obtained. The results obtained give the idea of structural-functional connections, due to which the self-organization appears in the metabolism running in a cell. The constructed mathematical model can be applied to the study of the toxic and allergic effects of drugs and various substances on cell metabolism.

Keywords: , , , , ,


References:

  1. Krebs HA, Johnson WA. The role of citric acid in intermediate metabolism in animal tissues. Enzymologia. 1937;4:148-156.
  2. Bohnensack R, Sel’kov EE. Stoichiometric regulation in the citric acid cycle. II. Non-linear interactions.  Studia Biophysica. 1977;66(1):47-63.
  3. Lyubarev AE, Kurganov BI. Supramolecular organization of enzymes of the tricarboxylic acid cycle. Mol Biol (Mosk). 1987 Sep-Oct;21(5):1286-96. Russian. PubMed
  4.  Kondrashova MN. Structuro-kinetic organization of the tricarboxylic acid cycle in the active functioning of mitochondria. Biofizika. 1989 May-Jun;34(3):450-8. Review. Russian. PubMed
  5. el-Mansi EM, Dawson GC, Bryce CF. Steady-state modelling of metabolic flux between the tricarboxylic acid cycle and the glyoxylate bypass in Escherichia coli. Comput Appl Biosci. 1994 Jun;10(3):295-9. PubMed, CrossRef
  6. Ramakrishna R, Edwards JS, McCulloch A, Palsson BO. Flux-balance analysis of mitochondrial energy metabolism: consequences of systemic stoichiometric constraints. Am J Physiol Regul Integr Comp Physiol. 2001 Mar;280(3):R695-704. PubMed
  7. Cortassa S, Aon MA, Marbán E, Winslow RL, O’Rourke B. An integrated model of cardiac mitochondrial energy metabolism and calcium dynamics. Biophys J. 2003 Apr;84(4):2734-55. PubMed, PubMedCentral, CrossRef
  8. Yugi K, Tomita M. A general computational model of mitochondrial metabolism in a whole organelle scale. Bioinformatics. 2004 Jul 22;20(11):1795-6. PubMed, CrossRef
  9. Singh VK, Ghosh I. Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tuberculosis, and its application to assessment of drug targets. Theor Biol Med Model. 2006 Aug 3;3:27. PubMed, PubMedCentral, CrossRef
  10. Mogilevskaya E, Demin O, Goryanin I. Kinetic model of mitochondrial Krebs cycle: unraveling the mechanism of salicylate hepatotoxic effects. J Biol Phys. 2006 Oct;32(3-4):245-71. PubMed, PubMedCentral, CrossRef
  11. Gachok VP. Kinetics of Biochemical Processes. Kiev: Nauk. Dumka, 1988. 219 p. (in Russian).
  12. Gachok VP. Strange Attractors in Biosystems. Kiev: Nauk. Dumka, 1989. 237 p. (in Russian).
  13. Armiger WB, Moreira AR, Phillips JA, Humphrey AE. Utilization of cellulose materials in inconventional food production. New York: Plenum Press, 1979.  P. 111–117.
  14. Monod J. Recherches sur la Croissanse des Cultures Bacteriennes. Paris: Hermann, 1942.
  15. Podgorskij VS. Physiology and Metabolism of Methanol-Assimilating Yeast. Kiev: Naukova Dumka, 1982. (in Russian).
  16. Drozdov-Tikhomirov L. N., Rakhimova N. T. The maximal biomass yield in yeast that assimilating methanol. Mikrobiologiya. 1986;55(5):775-780.
  17. Riznichenko GYu. Mathematical Models in Biophysics and Ecology. Moscow, Izhevsk: Inst. of Computer. Studies, 2003. (in Russian).
  18. Watteeuw CM, Armiger WB, Ristroph DL, Humphrey AE. Production of single cell protein from ethanol by fed-batch process. Biotechnol Bioeng. 1979 Jul;21(7):1221-1237. CrossRef
  19. Sel’kov EE. Self-oscillations in glycolysis. 1. A simple kinetic model. Eur J Biochem. 1968 Mar;4(1):79-86. PubMed, CrossRef
  20. Hess B, Boiteux A. Oscillatory phenomena in biochemistry. Annu Rev Biochem. 1971;40:237-58. Review. PubMed, CrossRef
  21. Goldbeter A, Lefever R. Dissipative structures for an allosteric model. Application to glycolytic oscillations. Biophys J. 1972 Oct;12(10):1302-15. PubMed, PubMedCentral, CrossRef
  22. Goldbeter A, Caplan SR. Oscillatory enzymes. Annu Rev Biophys Bioeng. 1976;5(1):449-76. Review. PubMed, CrossRef
  23. Gachok VP, Grytsay VI.  Dokl AN SSSR. 1985;282(1):51-53.
  24. Gachok VP, Grytsay VI, Arinbasarova AY, Medentsev AG, Koshcheyenko KA, Akimenko VK. Kinetic model of hydrocortisone 1-en-dehydrogenation by Arthrobacter globiformis. Biotechnol Bioeng. 1989 Feb 5;33(6):661-7. PubMed, CrossRef
  25. Gachok VP, Grytsay VI, Arinbasarova AY, Medentsev AG, Koshcheyenko KA, Akimenko VK. Kinetic model for the regulation of redox reaction in steroid transformation by Arthrobacter globiformis cells. Biotechnol Bioeng. 1989 Feb 5;33(6):668-80. PubMed, CrossRef
  26. Chaos in Chemical and Biochemical System / Ed. By R. Field, L. Györgyi.  Singapore: World Scientific, 1993.
  27. Kordium VA, Irodov DM, Maslova OO, Ruban TA, Sukhorada EM, Andrienko VI, Shuvalova NS, Likhachova LI, Shpilova SP. Fundamental biology reached a plateau – development of ideas. Biopolym Cell. 2011;27(6):480-498. CrossRef
  28. Kuznetsov S. P. Dynamical Chaos. Moscow: Nauka, 2001. (in Russian).
  29. Anishchenko V, Astakhov V, Neiman A. et al. Nonlinear Dynamics of Chaotic and Stochastic System. Tutorial and Modern Developments – Berlin: Springer, 2007.
  30. Grytsay VI. Self-organization in the macroporous gel structure with immobilized cells. Kinetic model for bioselective membrane of biosensor. Dopov NAN Ukr. 2000;(2):175-179.
  31. Grytsay VI. Self-organization in the biochemical process in immobilized cells of the bioselective membrane of a biosensor. Ukr J Phys. 2001;46(1):124-127.
  32. Grytsay VI, Andreev VV. The diffusion role on non-active structures formation in porous reaction-diffusion medium. Matem Modelir. 2006;18(12):88-94.
  33. Grytsay VI. Unsteady Conditions in Porous Reaction-Diffusion Medium. Romanian J Biophys. 2007;17(1):55-62.
  34. Grytsay VI.  The uncertainty in the evolution of structures of reaction-diffusion medium. Biophys Bull. 2007;(2(19)):92-97.
  35. Grytsay VI, Musatenko IV. The structure of a chaos of strange attractors within a mathematical model of the metabolism of a cell. Ukr J Phys. 2013;58(7):677-686. CrossRef
  36. Feigenbaum MJ. Quantitative universality for a class of nonlinear transformations. J Stat Phys. 1978;19(1):25-52. CrossRef
  37. Feigenbaum MJ. The universal metric properties of nonlinear transformations. J Stat Phys. 1979;21(6):669-706. CrossRef
  38. Feigenbaum MJ. The transition to aperiodic behavior in turbulent systems. Comm Math Phys. 1980;77(1):65-86. CrossRef

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License.