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Some realizations of (M, R)-systems and their interpretation

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Abstract

Some years ago (Rosen 1958a, b; 1959) we described a class of metaphorical, relational paradigms for cellular activity which we termed (M, R)-systems. A sizable amount of subsequent work, to be itemized below, has been devoted to an exploration of some of the properties of these systems. The main purpose of the present paper is to put this class of paradigms into a general system-theoretic perspective, with a particular view to appraising the relation between the type of system description embodied in the (M, R)-system and other kinds of physical and mathematical descriptions of cellular systems. Thus, the principal aim is to establish the relationships and connections between the global relational formalism embodied in the (M, R)-systems and the empirical descriptions which still represent the bulk of our biological knowledge.

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Literature

  • Arbib, M. 1965. “A Common Framework for Automata Theory and Control Theory.”J. SIAM Control, Ser. A,3, (No. 2), 206–222.

    Article  MATH  MathSciNet  Google Scholar 

  • — 1966. “Automata Theory and Control Theory—A Rapprochement.”Automatica,3, 161–189. Oxford, England: Pergamon Press.

    Google Scholar 

  • Higgins, J. 1967. “The Theory of Oscillating Reactions.”Industrial & Engineering Chemistry,59 (No. 5), 19–62.

    Article  Google Scholar 

  • Kalman, R. E. 1968. “New Developments in Systems Theory Relevant to Biology.”Systems Theory & Biology, edited by M. Mesarovich, pp. 222–232. New York: Springer-Verlag.

    Google Scholar 

  • Rosen, R. 1958a. “A Relational Theory of Biological Systems.”Bull. Math. Biophysics,20, 245–260.

    Google Scholar 

  • — 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories.”Ibid.,,20, 317–341.

    Google Scholar 

  • Rosen, R. 1959. “A Relational Theory of Biological Systems II.”Ibid.,,21, 109–128.

    Google Scholar 

  • — 1961. “A Relational Theory of Structural Changes Induced in Biological Systems by Alterations in Environments.”Ibid.,,23, 165–171.

    Google Scholar 

  • — 1962a. “A Note on Abstract Relational Biologies.”Ibid.,,24, 31–38.

    MATH  Google Scholar 

  • — 1963a. “On the Reversibility of Environmentally Induced Alterations in Abstract Biological Systems.”Ibid.,,25, 41–50.

    MATH  Google Scholar 

  • — 1963b. “Some Results in Graph Theory and Their Application to Abstract Relational Biology.”Ibid.,,25, 231–241.

    MATH  Google Scholar 

  • — 1964a. “Abstract Biological Systems as Sequential Machines.”Ibid.,,26, 103–111.

    MATH  Google Scholar 

  • — 1964b. “Abstract Biological Systems as Sequential Machines II: Strong Connectedness.”Ibid.,26, 239–246.

    MATH  Google Scholar 

  • — 1965. “Some Comments on Re-establishability.”Ibid.,,27, 11–14.

    Google Scholar 

  • — 1966a. “Biological and Physical Realizations of Abstract Metabolic Models.”Helgolander wiss. Meeresunters,14, 25–31.

    Article  Google Scholar 

  • — 1966b. “Abstract Biological Systems as Sequential Machines III: Some Algebraic Aspects.”Bull. Math. Biophysics,28, 141–148.

    MATH  Google Scholar 

  • — 1966c. “A Note on Replication in (M, R)-Systems.”Ibid.,,28, 149–151.

    MATH  Google Scholar 

  • — 1967a. “Two-Factor Models, Neural Nets and Biochemical Automata.”J. Theo. Biology,15, 282–297.

    Article  Google Scholar 

  • — 1967b. “Further Comments on Replication in (M, R)-Systems.”Bull. Math. Biophysics,29, 91–94.

    MATH  Google Scholar 

  • — 1967c. Monograph:Optimality Principles in Biology. (Russian Translation.) London: Butterworth & Co., Ltd.

    Google Scholar 

  • — 1968a. “Relational Biology and Cybernetics.”Biokybernetik Band,1, 49–55. Berlin: Gustav-Fischer Verlag.

    Google Scholar 

  • — 1968b. “Some Comments on the Physico-chemical Description of Biological Activity.”J. Theo. Biology,18, 380–386.

    Article  Google Scholar 

  • — 1968c. “On Analogous Systems.”Bull. Math. Biophysics,30, 481–492.

    MATH  Google Scholar 

  • — 1968d. “Turing’s Morphogens, Two-Factor Systems and Active Transport.”Ibid.,,30, 493–499.

    Google Scholar 

  • — 1969a. “Hierarchical Systems in Biology.” InHierarchical Structures, Wilson & Whyte. New York: American Elsevier.

    Google Scholar 

  • — 1969b. “Uber die Wahl der Zustandsvariablen für Metabilosche Systeme.”Studia Biophysica,14, 247–259.

    Google Scholar 

  • — 1970.Dynamical Systems in Biology. 2-volume Text-Monograph, Vol. 1, New York, N.Y.: John Wiley & Sons, Inc.

    Google Scholar 

  • Walter, C. F. 1969a. “Stability of Controlled Biological Systems.”J. Theo. Biology,23, 23–38.

    Article  Google Scholar 

  • — 1969b. “The Absolute Stability of Certain Types of Controlled Biological Systems.”Ibid.,,23, 39–52.

    Article  Google Scholar 

  • — 1970. “The Occurrence and the Significance of Limit Cycle Behavior in Controlled Biochemical Systems.”Ibid.,,27, 259–272.

    Article  Google Scholar 

  • Zadeh, L., and C. Desoer. 1963.Linear System Theory. New York: McGraw-Hill.

    MATH  Google Scholar 

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Rosen, R. Some realizations of (M, R)-systems and their interpretation. Bulletin of Mathematical Biophysics 33, 303–319 (1971). https://doi.org/10.1007/BF02476776

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  • DOI: https://doi.org/10.1007/BF02476776

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