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Oxygen diffusion in large single-celled organisms

The bulletin of mathematical biophysics volume 31, pages 327–340 (1969)Cite this article

Abstract

The functional relationship between the oxygen uptake rate of a spherical, single cell organism and the external oxygen tension is shown to be related to the dependence of the specific oxygen consumption rate, that is, the consumption rate of an infinitesimal volume element of cellular material, on the external oxygen tension. Analytical solutions of the governing steady state diffusion equation are obtained by dividing the system into three regions, an inner region of the sphere in which oxygen consumption rate depends upon oxygen tension, an outer region of the sphere in which oxygen consumption rate is constant (independent of oxygen tension), a nonconsuming membrane over the sphere that offers only resistance to oxygen diffusion, and an infinite region outside the sphere and membrane supplying oxygen to the system. The solutions show the oxygen tension as a function of position inside the spherical cell for a variety of system parameters.

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Literature

  • Adolph, E. F. 1929. “The Regulation of Adult Body Size in the Protozoan Colpoda.”J. of Experimental Zoology,53, 269–311.

    Article  Google Scholar 

  • — 1931.Regulation of Size. Springfield, Illinois: C. C. Thomas Company.

    Google Scholar 

  • Amberson, W. R. 1928. “The Influence of O2 Tension on the Respiration of Unicellular Organisms.”Bio. Bull.,55, 79–92.

    Google Scholar 

  • Chemical Engineers Handbook. 1963. Perry, J. H., ed. New York: McGraw Hill. pp. 14–21.

    Google Scholar 

  • Childress, J.J. 1968. “Oxygen Minimum Layer.”Science,160, 1242–3.

    Article  Google Scholar 

  • Davson, H. 1964.A Textbook of General Physiology, 3rd edition. Boston: Little Brown Company. pp. 12–14.

    Google Scholar 

  • Fatt, I. 1968. “Steady State Distribution of O2 and CO2 in thein vivo Cornea.”Exp. Eye Research,7, 413–430.

    Google Scholar 

  • Goldstick, T. K. 1966. Ph.D. Thesis, U. of California, Berkeley.

  • Hildebrand, F. B. 1962.Advanced Calculus for Applications. Princeton, N.J.: Prentice-Hall.

    MATH  Google Scholar 

  • Montgomery, H. A. C.et al. 1964. “Determination of Dissolved O2 by the Winkler Method and the Solubility of O2 in Pure Water and Sea Water.”J. Applied Chemistry (London),14, 280–96.

    Google Scholar 

  • Prosser, C. L. 1952.Comparative Animal Physiology, Philadelphia: W. B. Saunders & Company. p. 247.

    Google Scholar 

  • Rashevsky, N. 1960.Math. Biophysics, Vol. I. New York: Dover.

    Google Scholar 

  • Rose, G. and Quinn, J. A. 1967. “Composite Membranes: The Permeation of Gases through Deposited Monolayers.”Science,159, 636–7.

    Google Scholar 

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Affiliations

  1. Department of Chemical Engineering, University of California, Berkeley, California

    Thomas A. Massaro

  2. Department of Mechanical Engineering, University of California, Berkeley, California

    Irving Fatt

Authors
  1. Thomas A. Massaro
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  2. Irving Fatt
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Massaro, T.A., Fatt, I. Oxygen diffusion in large single-celled organisms. Bulletin of Mathematical Biophysics 31, 327–340 (1969). https://doi.org/10.1007/BF02477010

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  • DOI: https://doi.org/10.1007/BF02477010

Keywords

  • Oxygen Uptake
  • Oxygen Tension
  • Oxygen Diffusion
  • Oxygen Consumption Rate
  • Oxygen Uptake Rate