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The effects of cell density and metabolite flux on cellular dynamics

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Summary

Density-dependent regulation of cell growth in tissue culture is a well-known phenomenon but the mechanism of regulation remains obscure. Here we explore the effects of cell density and metabolite flux on the collective dynamics of a cell population. The intracellular dynamics are modelled by positive feedback kinetic mechanisms of the kind known to apply to yeast cells. Several experimental observations related to glycolytic oscillations are predicted and it is suggested that the general conclusions may be applicable in a broader context.

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References

  • Aldridge, J.: Short-range intercellular communication, biochemical oscillations, and circadian rhythms. In: Handbook of Engineering in Medicine and Biology (Fleming, ed.), Cleveland: Chemical Rubber Co. (1976)

    Google Scholar 

  • Aldridge, J., Pye, E. K.: Cell density dependence of oscillatory metabolism. Nature 259, 670 (1976)

    Google Scholar 

  • Betz, A.: Kinetics of yeast phosphofructokinase and the glycolytic oscillator. In: Biological and Biochemical Oscillators (Chance, B., Pye, E. K., Ghosh, A., Hess, B., eds.), New York: Academic Press (1973)

    Google Scholar 

  • Boiteux, A., Goldbeter, A., Hess, B.: Control of oscillating glycolysis of yeast by stochastic, periodic, and steady source of substrate: A model and experimental study. Proc. Nat. Acad. Sci. (USA) 72, 3829–3833 (1975)

    Google Scholar 

  • Eagle, H., Piez, K.: The population-dependent requirement by cultured mammalian cells for metabolites which they can synthesize. J. Exp. Med. 116, 29–43 (1962)

    Google Scholar 

  • Folkman, J., Greenspan, H. P.: Influence of geometry on control of cell growth. Biochim. et Biophys. Acta 417, 211–236 (1975)

    Google Scholar 

  • Furshpan, E. J., Potter, D. D.: Low resistance junctions between cells in embryos and tissue culture. Curr. Top. Devel. Biol. 3, 95–127 (1968)

    Google Scholar 

  • Gibbs, R. G., Murray, J. D.: On models of oscillations in the glycolytic pathway. Preprint (1976)

  • Hartman, P.: Ordinary Differential Equations. Baltimore P. Hartman (1973)

    Google Scholar 

  • Hess, B., Boiteux, A.: Substrate control of glycolytic oscillations, in Biological and Biochemical Oscillators (Chance, B. et. al., eds.) New York: Academic Press, (1973)

    Google Scholar 

  • Higgins, J.: Oscillating reactions. Ind. and Eng. Chem. Fund. 59, 19–62 (1967)

    Google Scholar 

  • Hoffman, R., Ristow, H. J., Veser, J., Frank, W.: Properties of two growth-stimulating proteins isolated from fetal calf serum. Exp. Cell. Res. 80, 275–280 (1973)

    Google Scholar 

  • Holley, R. W.: Control of growth of mammalian cells in cell culture. Nature 258, 487–490 (1975)

    Google Scholar 

  • Holley, R. W., Kiernan, J.: Control of the initiation of DNA synthesis in 3T3 cells: low molecular-weight nutrients. Proc. Nat. Acad. Sci. (USA) 71, 2942–2945 (1974)

    Google Scholar 

  • Hopf, E.: Abzweigung einer periodischen losung von einer stationaren losung eines differential Systems. Ber. Math.-Phys. Klasse Sachs. Akad. Wiss. Leipzig 94, 3–22 (1942)

    Google Scholar 

  • Konigsberg, I. R.: Diffusion-mediated control of myoblast fusion. Dev. Biol. 26, 133–152 (1971)

    Google Scholar 

  • Loewenstein, W. R., Kanno, Y.: Intercellular communication and the control of tissue growth. Lack of communication between cancer cells. Nature 209, 1248–1249 (1966)

    Google Scholar 

  • Loewenstein, W. R.: Emergence of order in tissues and organs. Dev. Biol. Supp. 2, 151–183 (1968)

    Google Scholar 

  • Luss, D.: The influence of capacitance terms on the stability of lumped and distributed parameter systems. Chem. Eng. Sci. 29, 1832–1836 (1974)

    Google Scholar 

  • Machemer, H., Eckert, R.: Electrophysiological control of reversed ciliary beating in Paramecium. J. Gen. Physiol. 61, 572–587 (1973)

    Google Scholar 

  • Othmer, H. G., Scriven, L. E.: Instability and dynamic pattern in cellular networks. J. Theor. Biol. 32, 507–537 (1971)

    Google Scholar 

  • Othmer, H. G., Scriven, L. E.: Nonlinear aspects of dynamic pattern in cellular networks. J. Theor. Biol. 43, 87–112 (1974)

    Google Scholar 

  • Othmer, H. G.: Current problems in pattern formation. In Lects. on Math. in Life Sci. 9, (S. Levin, ed.) Providence: American Mathematical Society (1977)

    Google Scholar 

  • Othmer, H. G.: On the significance of finite propagation speeds in multicomponent reacting systems. J. Chem. Phys. 64, 469–470 (1976)

    Google Scholar 

  • Othmer, H. G.: The structure of kinetic mechanisms that can lead to oscillations in coupled cells, in preparation (1977b)

  • Perelson, A.: A note on the qualitative theory of lumped parameter systems. Chem. Eng. Sci. 31, 170–173 (1976)

    Google Scholar 

  • Poore, A.: On the theory and application of Hopf-Friedrichs bifurcation theory. Arch. Rat. Mech. Anal. 60, 371–393 (1976)

    Google Scholar 

  • Pye, E. K.: Periodicities in intermediary metabolism. In: Symp. on Biochronometry, Washington: Nat. Acad. Sci. Press (1971)

    Google Scholar 

  • Ruelle, D., Takens, F.: On the nature of turbulence. Comm. Math. Phys. 20, 167–192 (1971)

    Google Scholar 

  • Sanford, K. K., Earle, W. R., Likely, G. D.: The growth in vitro of single isolated tissue cells. J. Nat. Cancer Inst., 9, 229–246 (1948)

    Google Scholar 

  • Sefton, B., Rubin, H.: Stimulation of glucose transport in cultures of density-inhibited chick embryo cells. Proc. Nat. Acad. Sci. (USA) 68, 3154–3157 (1971)

    Google Scholar 

  • Spiegelman, S.: Physiological competition as a regulatory mechanism in morphogenesis. Quart. Rev. Biol. 20, 121–146 (1945)

    Google Scholar 

  • Stoker, M. G. P.: Role of diffusion boundary layer in contact inhibition of growth. Nature 246, 200–203 (1973)

    Google Scholar 

  • Wilcox, M., Mitchison, G., Smith, R.: Pattern formation in the blue-green alga Anabena. J. Cell Sci. 12, 707–723 (1973)

    Google Scholar 

  • Cohen, R., Pacifici, M., Rubinstein, N., Biehl, J., Holtzer, H.: Effect of a tumor promotor on myogenesis. Nature 266, 538–540 (1977)

    Google Scholar 

  • Shymko, R. M., Glass, L.: Cellular and geometric control of tissue growth and mitotic in stability. Jour. Theor. Biol. 63, 355–374 (1976)

    Google Scholar 

  • Nicolas, J. F., Dubois, P., Jakob, H., Gaillard, J., Jacob, F.: Tératocarcinome de la souris: différenciation en culture d'une lignée de cellules primitives a potentialités multiples. Ann. de Microbiologie 126A, 3–22 (1976)

    Google Scholar 

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Othmer, H.G., Aldridge, J.A. The effects of cell density and metabolite flux on cellular dynamics. J. Math. Biology 5, 169–200 (1978). https://doi.org/10.1007/BF00275897

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