Molecular and Cellular Biochemistry

, Volume 120, Issue 1, pp 1–13 | Cite as

An allometric interpretation of the spatio-temporal organization of molecular and cellular processes

  • Miguel Antonio Aon
  • Sonia Cortassa


Different levels of organization distinguished by characteristics spatial dimensions, Ec, and relaxation times, Tr, of biological processes ranging from electron transport in energy transduction to growth of microbial and plant cells, are shown to be related through a relation that may be interpreted as allometric and characterized by two different slopes. Processes, at levels of organization occurring in spatial dimensions of micrometers and relaxing in the order of minutes, delimit a ‘transition point’ between the two curves, that we interpret as a limit for the emergence of macroscopic coherence. The characteristic spatial dimension, Ec, and the relaxation time, Tr, contain dynamical information about the processes occurring at a given level of organization. When a steady state of a biological process at a certain level of organization becomes unstable, the system undergoes a transition to another level of organization. To exemplify the appearance of macroscopic order at levels of organization further from the ‘transition point’ we present in this report various experimental systems involving many levels of organization allometrically related that exhibit different kinds of self-organized behavior, i.e. bistability, oscillations, changes in (a)symmetry.

Key words

dynamical organization levels of organization allometry bistability oscillations asymmetry changes 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Landau LD, Lifschitz EM: Statistical Physics. Pergamon Press, New York, 1969Google Scholar
  2. 2.
    Haken H: In: FE Yates, A Garfinkel, DO Walter and GB Yates (eds) Self-Organizing Systems. The emergence of order. Plenum Press, New York and London, 1987, pp 417–434Google Scholar
  3. 3.
    Nicolis G, Prigogine I: Self-organization in non-equilibrium systems. John Wiley & Sons, New York, 1977, pp 375–379Google Scholar
  4. 4.
    Peacoke AR: The Physical Chemistry of Biological Organization. Clarendon Press, Oxford, 1983, pp 245–268Google Scholar
  5. 5.
    Churchland PS, Sejnowski TJ: Perspectives on cognitive neuroscience. Science 242:741–745, 1988Google Scholar
  6. 6.
    Aon MA, Cortassa S: The regulation of plant cell growth: A bioelectromechanochemical model. J theor Biol 138:429–457, 1989Google Scholar
  7. 7.
    Cortassa S, Sun H, Kernevez JP, Thomas D: Pattern formation in an immobilized bienzyme system. A morphogenetic model. Biochem J 269:115–122, 1990Google Scholar
  8. 8.
    Verdoni N, Aon MA, Lebeault JM, Thomas D: Proton motive force, energy recycling by end product excretion and metabolic uncoupling during anaerobic growth ofPseudomonas mendocina. J Bacteriol 172:6673–6681, 1990Google Scholar
  9. 9.
    Aon MA, Thomas D, Hervagault JF: Spatial patterns in a photobiochemical system. Proc Natl Acad Sci USA 85:516–519, 1989Google Scholar
  10. 10.
    Aon MA, Cortassa S, Westerhoff HV, Berden JA, van Spronsen E, van Dam K: Dynamic regulation of yeast glycolytic oscillations by mitochondrial functions. J Cell Sci 99:325–334, 1991Google Scholar
  11. 11.
    Cortassa S, Aon MA, Thomas D: Thermodynamic and kinetic studies of a stoichiometric model of energetic metabolism under starvation conditions. FEMS Microbiol Lett 66:249–256, 1990Google Scholar
  12. 12.
    Aon MA, Cortassa S: Thermodynamic evaluation of energy metabolism in mixed substrate catabolism: Modeling studies of stationary and oscillatory states. Biotechnol and Bioeng 137:197–204, 1991Google Scholar
  13. 13.
    Aon MA, Cortassa S, Westerhoff HV, van Dam K: Synchrony and mutual stimulation of yeast cells during fast glycolytic oscillations. J Gen Microbiol 138 (in the press), 1992Google Scholar
  14. 14.
    Higgins J: Dynamics and controls in cellular reactions. In: B Chance, RW Estabrook and R Williamson (eds) Control of energy metabolism. Academic Press, New York, 1965, pp 13–46Google Scholar
  15. 15.
    Aon MA, Cortassa S, Hervagault JF, Thomas D: pH-induced bistable dynamic behaviour in the reaction catalysed by glucose-6-phosphate dehydrogenase and conformational hysteresis of the enzyme. Biochem J 262:795–800, 1989Google Scholar
  16. 16.
    Cortassa S, Aon MA, Westerhoff H: Linear nonequilibrium thermodynamics describes the dynamics of an autocatalytic system. Biophys J 60:794–803, 1991Google Scholar
  17. 17.
    Kernevez JP: Enzyme Mathematics. North Holland, Amsterdam, 1980Google Scholar
  18. 18.
    Chance B, Estabrook RW, Ghosh A: Damped sinusoidal oscillations of cytoplasmic reduced pyridine nucleotides in yeast cells. Proc Natl Acad Sci USA 51:1244–1251, 1964Google Scholar
  19. 19.
    Hess B, Boiteux A: Substrate control of glycolytic oscillations. In: B Chance, K Pye, AK Ghosh and B Hess (eds) Biological and Biochemical Oscillators. Academic Press, New York, 1973, pp 229–242Google Scholar
  20. 20.
    Kirschner M, Mitchinson T: Beyond self-assembly: from microtubules to morphogenesis. Cell 45:329–342, 1986Google Scholar
  21. 21.
    Thom R: Stabilite Structurelle et Morphogenese, Intereditions, Paris, 1972Google Scholar
  22. 22.
    Guckenheimer J, Holmes P: Nonlinear Oscillations, Dynamical Systems and Bifurcation Vector Fields, Springer Verlag, New York, 1983Google Scholar
  23. 23.
    Lewis J, Slack JM, Wolpert L: Thresholds in development. J theor Biol 65:579–590, 1977Google Scholar
  24. 24.
    Abraham RH: Dynamics and self-organization. In: FE Yates, A Garfinkel, DO Walter and GB Yates (eds) Self-Organizing Systems. The emergence of order. Plenum Press, New York and London, 1987, pp 599–613Google Scholar
  25. 25.
    Glass L, Mackey MC: From clocks to chaos. The rhythms of life. Princeton University Press, Princeton, New Jersey, 1988, p 172Google Scholar
  26. 26.
    Rabouille C, Cortassa S, Aon MA: Fractal organization in biological macromolecular lattices. J Biomol Struct & Dynamics 9: 1013–1024, 1992Google Scholar
  27. 27.
    Fersht A: Estructura y Mecanismo de los Enzimas. Ed Reverte, Barcelona, 1980, pp 104–135Google Scholar
  28. 28.
    Careri G, Fasella P, Gratton E: Enzyme dynamics: the statistical physics approach. Ann Rev Biophys Bioengin 8:69–97, 1979Google Scholar
  29. 29.
    Batke J: Channeling of glycolytic intermediates by temporary, stationary bi-enzyme complexes is probablein vivo. Trends Biochem Sci 14:481–482, 1989Google Scholar
  30. 30.
    Clegg JS: Properties and metabolism of the aqueous cytoplasm and its boundaries. Am J Physiol 246:R133-R151, 1984Google Scholar
  31. 31.
    Ottaway JH, Mowbray J: The role of compartmentation in the control of glycolysis. Curr Top Cell Regul 107–208, 1977Google Scholar
  32. 32.
    Srisvatava DK, Bernhard SA: Metabolite transfer via enzymeenzyme complexes. Science 234:1081–1086, 1987Google Scholar
  33. 33.
    Ingraham JL, Maaloe O, Neidhardt FC: Growth of the Bacterial Cell. Sihauer Assoc., Inc Sunderland, Massachusetts, 1983, pp 267–315Google Scholar
  34. 34.
    Maloney PC, Kashket ER, Wilson TH: Methods for studying transport in bacteria. In: ED Korn (ed). Methods in Memb Biol 5: 1–49, 1975Google Scholar
  35. 35.
    Bailey JE, Ollis DF: Biochemical Engineering Fundamentals. McGraw-Hill, New York, p 269, 1977Google Scholar
  36. 36.
    Thompson J, Torchia DA: Use of31P nuclear magnetic resonance spectroscopy and14C fluorography in studies of glycolysis and regulation of pyruvate kinase inStreptococcus lactis. J Bacteriol 158:791–800, 1984Google Scholar
  37. 37.
    Linker C, Wilson HT: Cell volume regulation inMycoplasma gallisepticum. J Bacteriol 163:1243–1249, 1985Google Scholar
  38. 38.
    Linker C, Wilson HT: Sodium and proton transport inMycoplasma gallisepticum. J Bacteriol 163:1250–1257, 1985Google Scholar
  39. 39.
    Atkinson B, Mavituna F: Biochemical Engineering and Biotechnology Handbook. Mcmillan Publishers, 1983, pp 402–408Google Scholar
  40. 40.
    Volkenshtein MV: Biofisica. Ed Mir, Moscu, 1985, pp 478–497Google Scholar
  41. 41.
    Polle A, Junge W: Biophys J 56:27–31, 1989Google Scholar
  42. 42.
    Kooten OV, Snell JFH, Vredenberg WJ: Photosynthetic free energy transduction related to the electric potential changes across the thylakoid membrane. In: M. Nijhoff, W. Junk (eds). Photosynthesis Research. Dordrecht, The Netherlands, 1986, pp 211–227Google Scholar
  43. 43.
    Michels PAM, Michels JPJ, Boonstra J, Konings WN: Generation of an electrochemical proton gradient in bacteria by the excretion of metabolic end products. FEMS Microbiol Lett 5: 357–364, 1979Google Scholar
  44. 44.
    Smith RL, Oldfield E: Dynamic structures of membranes by deuterium NMR. Science 225:280–288, 1984Google Scholar
  45. 45.
    Falke LC, Edwards KL, Pickard BG, Misler S: A strecht-activated anion channel in tobacco protoplasts. FEBS Lett. 237:141–144, 1988Google Scholar
  46. 46.
    Oosawa F, Asakura S: Thermodynamics of the Polymerization of Protein. Academic Press, 1975, pp 90–103Google Scholar
  47. 47.
    Theologis A: Rapid gene regulation by auxin. Ann Rev Pl Physiol 37:407–438, 1986Google Scholar
  48. 48.
    Baochong G, Weisenberg RC: Characterization of a microtubule-stimulated adenosinetriphosphatase activity associated with microtubule gelation-contraction. Biochemistry 27:5032–5038, 1988Google Scholar
  49. 49.
    Menegus F, Cattaruzza L, Chersi A, Fronza G: Differences in the anaerobic lactate-succinate production and in the changes of cell sap pH for plants with high and low resistance to anoxia. Pl Physiol 90:29–32, 1989Google Scholar
  50. 50.
    Rosen R: Dynamical System Theory in Biology. John Wiley & Sons, New York, vol I, 1970Google Scholar
  51. 51.
    von Bertalanffy L: Theorie Generale des Systemes. Dunod, Paris, 1968, pp 168–176Google Scholar
  52. 52.
    Rosen R: Optimality Principles in Biology. Butterworths, London, 1967Google Scholar
  53. 53.
    Reiss MJ: The allometry of growth and reproduction. Cambridge University Press, Cambridge, 1989Google Scholar
  54. 54.
    Pagel MD, Harvey PH: Taxonomic differences in the scaling of brain on body weight among mammals. Science 244:1589–1593, 1989Google Scholar
  55. 55.
    Sernetz M, Gelleri M, Hofmann J: The organism as bioreactor. Interpretation of the reduction law of metabolism in terms of heterogeneous catalysis and fractal structure. J theor Biol 117: 209–230, 1985Google Scholar
  56. 56.
    Pratt O: Ecuaciones Diferenciales Ordinarias. Ed. Reverte, Barcelona, 1974Google Scholar
  57. 57.
    Savageau MA: Biochemical Systems Analysis. Addison-Wesley, Reading, Massachusetts, 1976Google Scholar
  58. 58.
    Kauffman SA: Adaptation on rugged fitness landscapes. In: D Stein (ed) Lectures in the sciences of complexity. Addison-Wesley Publishing Company, Santa Fe Institute, 1989, pp 527–712Google Scholar
  59. 59.
    Waddington CH: Organisers and Genes. Cambridge, University Press, London, 1947Google Scholar
  60. 60.
    Verdoni N, Aon MA, Lebeault JM: Metabolic and energetic control ofPseudomonas mendocina growth during transitions from aerobic to oxygen-limited conditions in chemostat cultures. Appl Environm Microbiol 58:3150–3156, 1992Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Miguel Antonio Aon
    • 1
  • Sonia Cortassa
    • 1
  1. 1.Instituto Superior de Investigaciones Biológicas (INSIBIO-CONICET), Departamento Bioquímica de la NutriciónUniversidad Nacional de TucumánTucumánArgentina

Personalised recommendations