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A relational theory of biological systems

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The relational phenomena exhibited by metabolizing systems may be considered as special cases of those exhibited by a more general class of systems. This class is specified, and some of tis properties developed. An attempt is then made to apply these properties to a theory of metabolism by suitable specialization. A number of biologically significant theorems are obtained which apply directly to the theory of the free-living single cell. Among the results obtained are the following: On the basis of our model, there must always exist a component of the system which cannot be replaced or repaired by the system in the event of its inhibition or destruction. Under certain conditions, a metabolizing system possesses a component the inhibition of which will completely terminate the metabolic activity of the system. Furthermore a number of other diverse phenomena, such as the effects of a deficient environment, encystment phenomena, and even an indication of why a metabolizing system which represents a cell should possess a nucleus, follow in a straightforward fashion from our model.

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  • Calkins, G. N. 1926.The Biology of the Protozoa. New York: Lea and Febiger.

    Google Scholar 

  • Cohn, David. 1954. “Optimal Systems: I. The Vascular System.”Bull. Math. Biophysics,16, 59–74.

    Article  Google Scholar 

  • —. 1955. “Optimal Systems: II. The Vascular System.”,17, 219–27.

    Article  Google Scholar 

  • Hall, A. D. and R. E. Fagen. 1956. “Definition of System.” Yearbook of the Society for the Advancement of General Systems Theory, Volume I.

  • Rashevsky, N. 1948.Mathematical Biophysics. Rev. Ed. Chicago; University of Chicago Press.

    MATH  Google Scholar 

  • —. 1954. “Topology and Life.”Bull. Math. Biophysics,16, 317–48.

    MathSciNet  Google Scholar 

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Rosen, R. A relational theory of biological systems. Bulletin of Mathematical Biophysics 20, 245–260 (1958).

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