The bulletin of mathematical biophysics

, Volume 27, Supplement 1, pp 15–19 | Cite as

On compartmentalization

  • Vojtech Ličko
Article

Abstract

The notion of a compartment is discussed in terms of the Markovian process. From the stochastic matrix (the elements of which are state transition probabilities between different states of a particle of a chemical element), one may find a (generally) nonstochastic matrix; the elements of this second matrix are probabilities that, starting from some initial state, the particle will reach another seleced state (W. Feller, 1962,An Introduction to Probability Theory). Forming equivalence classes of states it can be shown that the equivalence classes based on an equivalence relation, which holds for the elements of the above-mentioned nonstochastic matrix, are essential for the notion of a compartment. From this procedure it is also obvious that a rigorous definition of a physically realizable compartment is impossible. Some conclusions on the practical use of compartmental analysis are drawn.

Keywords

Equivalence Class Chemical Element Biophysics VOLUMe Stochastic Matrix State Transition Probability 

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Literature

  1. Bergner, P. E. E. 1961. “Tracer Dynamics. I. A. Tentative Approach and Definition of Fundamental Concepts.”Jour. Theoret. Biol.,2, 120–140.CrossRefMathSciNetGoogle Scholar
  2. Feller, W. 1962.An Introduction to Probability Theory and Its Applications, Vol. I, second edition. New York: John Wiley & Sons, Inc.Google Scholar
  3. Rescigno, A. 1960. “Synthesis of a Multicompartmented Biological Model.”Biochim. Biophys. Acta,37, 463–468.CrossRefGoogle Scholar

Copyright information

© N. Rashevsky 1965

Authors and Affiliations

  • Vojtech Ličko
    • 1
  1. 1.Institute of Endocrinology of the Slovak Academy of SciencesBratislavaCzechoslovakia

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