Multifractality in intracellular enzymatic reactions

Journal of Theoretical Biology

Volumn 240, Issue 2, 2006, Pages 209-217

  Aranda, Juan S ^a   Salgado, Edgar ^a   Muñoz Diosdado, Alejandro ^a  

^a INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

Author keywords

Enzymatic reactions; Fractal kinetics; Multifractality; Stochastic simulation

Indexed keywords

CATALYSIS; CYTOPLASM; DIFFUSION; ENZYME; ENZYME ACTIVITY; REACTION KINETICS; STOCHASTICITY;

ARTICLE; CELL STRUCTURE; CHEMICAL REACTION KINETICS; CULTURE MEDIUM; CYTOPLASM; DIFFUSION; ENZYME KINETICS; ENZYME MECHANISM; MATHEMATICAL MODEL; MICHAELIS MENTEN KINETICS; PRIORITY JOURNAL; STOCHASTIC MODEL; THEORETICAL MODEL;

ANIMALS; CATALYSIS; CELLS; COMPUTER SIMULATION; ENZYMES; FRACTALS; MODELS, BIOLOGICAL; MODELS, CHEMICAL; MODELS, STATISTICAL;

EID: 33646086005     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2005.09.005     Document Type: Article

References (35)

1. Althaus I.W., Chou J.J., Gonzales A.J., Diebel M.R., Chou K.C., Kezdy F.J., Romero D.L., Palmer J.R., Thomas R.C., Aristoff P.A., Tarpley W.G., and Reusser F. Kinetic studies with the non-nucleoside HIV-1 reverse transcriptase inhibitor U-88204E. Biochemistry 32 (1993) 6548-6554
2. Aon M.A., O'Rourke B., and Cortassa S. The fractal architecture of cytoplasmic organisation: scaling, kinetics and emergence in metabolic networks. Mol. Cell. Biochem. 256/257 (2004) 169-184
3. Berry H. Monte Carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation. Biophys. J. 83 (2002) 1891-1901
4. Bolis C.L., and Licino J. The Autonomic Nervous System (1999), World Health Organization, Geneva, Switzerland
5. Briggs G.E., and Haldane J.S.B. A criticism of Michaelis and Menten's equation for enzyme action. Biochem. J. 19 (1925) 338-339
6. Chhabra A., and Jensen R.V. Direct determination of the f(α) singularity spectrum. Phys. Rev. Lett. 62 (1989) 1327-1330
7. Chhabra A., Menevau C., Jensen R.V., and Sreenivasan K.R. Direct determination of the f(α) singularity spectrum and its application to fully developed turbulence. Phys. Rev. A 40 (1989) 5284-5294
8. Chou K.C. Graphic rules in steady and non-steady state enzyme kinetics. J. Biol. Chem. 264 (1989) 12074-12079
9. Chou K.C., and Zhou G.P. Role of the protein outside active site on the diffusion-controlled reaction of enzyme. J. Am. Chem. Soc. 104 (1982) 1409-1413
10. Coppens, M.O., Mandelbrot, B.B., 1999. Easy and natural generation of multifractals: multiplying harmonics of periodic functions. In: Fractals in Engineering Delft Conference, pp. 113-121.
11. Eckmann J.P., and Kamphorst S.O. Lyapunov exponents from time series. Phys. Rev. A 34 (1986) 4971-4979
12. Eckmann J.P., and Ruelle D. Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57 (1985) 617-656
13. Firth C.A.J.M., and Bray D. Stochastic simulation of cell signaling pathways. In: Bower J.M., and Bolouri H. (Eds). Computational Modeling of Genetic and Biochemical Networks (2001), MIT Press, USA 263-286
14. Garcia-Viloca M., Gao J., Karplus M., and Truhlar D.G. How enzymes work: analysis by modern rate theory and computer simulations. Science 303 (2004) 186-195
15. Gillespie D.T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81 (1977) 2340-2361
16. Hammes G.G. Multiple conformational changes in enzyme catalysis. Biochemistry 41 (2002) 8221-8228
17. Henri V. Recherches sur la loi de l'action de la sucrase. C.R. Hebd. Acad. Sci. 133 (1901) 891-899
18. Henri V. Théorie générale de l'action de quelques diastases. C.R. Hebd. Acad. Sci. 135 (1902) 916-919
19. Kopelman R. Rate processes on fractals: theory, simulations, and experiments. J. Stat. Phys. 42 (1986) 185-200
20. Kopelman R. Fractal reaction kinetics. Science 241 (1988) 1620-1626
21. Kuzmič P., Ng K.Y., and Heath T.D. Mixtures of tight-binding enzyme inhibitors: kinetic analysis by a recursive rate equation. Anal. Biochem. 200 (1992) 68-73
22. Laidler K.J. A brief history of enzyme kinetics. In: Cornish-Bowden A. (Ed). New Beer in an Old Bottle: Eduard Buchner and the Growth of Biochemical Knowledge (1997), Universitat de València, Valencia, Spain 127-133
23. Li H., and Wang F. Protein conformation and enzymatic kinetics. In: Iannaccone P.M., and Khokha M. (Eds). Fractal Geometry in Biological Systems (1996), CRC Press, USA 57-123
24. Lin A.L., Feldman M.A., and Kopelman R. Spatially resolved anomalous kinetics of a catalytic reaction: enzymatic glucose oxidation in capillary spaces. J. Phys. Chem. 101 (1997) 7881-7884
25. López-Quintela A., and Casado J. Revision of the methodology in enzyme kinetics: a fractal approach. J. Theor. Biol. 139 (1989) 129-139
26. Mandelbrot B.B. The fractal geometry of nature (1983), W.H. Freeman, New York, USA
27. Matías M.A., and Güémez J. On the effects of molecular fluctuations on models of chemical chaos. J. Chem. Phys. 102 (1995) 1597-1606
28. Michaelis L., and Menten M.L. Kinetik der invertinwirkung. Biochem. Z. 110 (1913) 217-233
29. Roux J.C., Simoyi R.H., and Swinney H.L. Observation of a strange attractor. Physica 8D (1983) 257-266
30. Savageau M.A. Michaelis-Menten mechanism revisited: implications of fractal kinetics. J. Theor. Biol. 176 (1995) 115-124
31. max estimates. Commun. Theor. Biol. 8 (2003) 169-187
32. Schnell S., and Turner T.E. Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Prog. Biophys. Mol. Biol. 85 (2004) 235-260
33. Turner T.E., Schnell S., and Burrage K. Stochastic approaches for modelling in vivo reactions. Comp. Biol. Chem. 28 (2004) 165-178
34. Verkman A.S. Solute and macromolecule diffusion in cellular aqueous compartments. Trends Biochem. Sci. 27 (2002) 27-33
35. Wolf A., Swift J.B., Swinney H.L., and Vastano J.A. Determining Lyapunov exponents from time series. Physica 16D (1985) 285-317